『同期現象の科学』参考文献
M. M. Abdulrehem and E. Ott,
Low dimensional description of pedestrian-induced oscillation of the Millennium Bridge,
Chaos 19, 013129 (2009). [Journal] [arXiv]
[cited in pages: 245, 284]
D. M. Abrams and S. H. Strogatz,
Chimera states for coupled oscillators,
Phys. Rev. Lett. 93, 174102 (2004). [Journal] [arXiv]
[cited in pages: 259, 264]
D. M. Abrams and S. H. Strogatz,
Chimera states in a ring of nonlocally coupled oscillators,
Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, 21 (2006). [Journal] [arXiv]
[cited in page: 264]
D. M. Abrams, R. E. Mirollo, S. H. Strogatz, and D. A. Wiley,
Solvable model for chimera states of coupled oscillators,
Phys. Rev. Lett. 101, 084103 (2008). [Journal] [arXiv]
[cited in pages: 271, 272, 282, 317]
J. A. Acebron, L. L. Bonilla, C. J. Perez Vicente, F. Ritort, and R. Spigler,
The Kuramoto model: A simple paradigm for synchronization phenomena,
Rev. Mod. Phys. 77, 137 (2005). [Journal]
[cited in page: 232]
I. Aihara,
Modeling synchronized calling behavior of Japanese tree frogs,
Phys. Rev. E 80, 011918 (2009). [Journal]
[cited in page: 6]
I. Aihara, R. Takeda, T. Mizumoto, T. Otsuka, T. Takahashi, and H. G. Okuno, and K. Aihara,
Complex and transitive synchronization in a frustrated system of calling frogs,
Phys. Rev. E 83, 031913 (2011). [Journal]
[cited in pages: 6, 7]
I. Aihara, T. Mizumoto, T. Otsuka, H. Awano, K. Nagira, H. G. Okuno, and K. Aihara,
Spatio-temporal dynamics in collective frog choruses examined by mathematical modeling and field observations,
Sci. Rep. 4, 3891 (2014). [Journal]
[cited in pages: 6, 7]
T. M. Antonsen, R. T. Faghih, M. Girvan, E. Ott, and J. H. Platig,
External periodic driving of large systems of globally coupled phase oscillators,
Chaos 18, 037112 (2008). [Journal] [arXiv]
[cited in page: 284]
S. Aoi, T. Yamashita, and K. Tsuchiya,
Hysteresis in the gait transition of a quadruped investigated using simple body mechanical and oscillator network models,
Phys. Rev. E 83, 061909 (2011). [Journal]
[cited in page: 32]
T. Aoyagi, T. Takekawa, and T. Fukai,
Gamma rhythmic bursts: coherence control in networks of cortical pyramidal neurons,
Neural Comput. 15, 1035 (2003). [Journal]
[cited in page: 162]
K. Arai and H. Nakao,
Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses,
Phys. Rev. E 77, 036218 (2008). [Journal] [arXiv]
[cited in page: 195(2)]
I. S. Aranson and L. Kramer,
The world of the complex Ginzburg-Landau equation,
Rev. Mod. Phys. 74, 99 (2002). [Journal] [arXiv]
[cited in pages: 73, 100]
A. Arenas, A. Diaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou,
Synchronization in complex networks,
Phys. Rep. 469, 93 (2008). [Journal] [arXiv] [Author]
[cited in page: 32]
J. T. Ariaratnam and S. H. Strogatz,
Phase diagram for the Winfree model of coupled nonlinear oscillators,
Phys. Rev. Lett. 86, 4278 (2001). [Journal] [arXiv]
[cited in page: 231]
A. Arneodo, P. Coullet, and C. Tresser,
A possible new mechanism for the onset of turbulence,
Phys. Lett. A 81, 197 (1981). [Journal]
[cited in page: 124]
P. Ashwin, O. Burylko, and Y. Maistrenko,
Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators,
Physica D 237, 454 (2008). [Journal]
[cited in page: 228]
N. Bagheri, J. Stelling, and F. J. Doyle III,
Circadian phase resetting via single and multiple control targets,
PLoS Comput. Biol. 4, e1000104 (2008). [Journal]
[cited in page: 145]
G. Barlev, T. M. Antonsen, and E. Ott,
The dynamics of network coupled phase oscillators: An ensemble approach,
Chaos 21, 025103 (2011). [Journal]
[cited in page: 284]
E. Barreto, B. R. Hunt, E. Ott, and P. So,
Synchronization in networks of networks:
The onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators,
Phys. Rev. E 77, 036107 (2008). [Journal]
[cited in page: 317]
D. Battogtokh and A. S. Mikhailov,
Controlling turbulence in the complex Ginzburg-Landau equation,
Physica D 90, 84 (1996). [Journal]
[cited in page: 67]
N. Bekki and K. Nozaki,
Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation,
Phys. Lett. A 110, 133 (1985). [Journal]
[cited in page: 107]
T. B. Benjamin and J. E. Feir,
The disintegration of wave trains on deep water,
J. Fluid Mech. 27, 417 (1967). [Journal]
[cited in page: 81]
M. Bennett, M. F. Scatz, H. Rockwood, and K. Wiesenfeld,
Huygens's clocks,
Proc. R. Soc. London A 458, 563 (2002). [Journal]
[cited in page: 6]
C. Bick, M. Timme, D. Paulikat, D. Rathlev, and P. Ashwin,
Chaos in symmetric phase oscillator networks,
Phys. Rev. Lett. 107, 244101 (2011). [Journal] [arXiv]
[cited in page: 228]
N. Biggs,
Algebraic potential theory on graphs,
Bull. London Math. Soc. 29, 641 (1997). [Journal]
[cited in page: 319]
K. A. Blaha, A. Pikovsky, M. Rosenblum, M. T. Clark, C. G. Rusin, and J. L. Hudson,
Reconstruction of two-dimensional phase dynamics from experiments on coupled oscillators,
Phys. Rev. E 84, 046201 (2011). [Journal]
[cited in page: 168]
S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. Zhou,
The synchronization of chaotic systems,
Phys. Rep. 366, 1 (2002). [Journal]
[cited in page: 5]
N. N. Bogoliubov and Y. A. Mitropolsky,
Asymptotic Methods in the Theory of Non-Linear Oscillations
(Gordon and Breach, New York, 1961). [Amazon]
[益子正教 訳: 非線型振動論 - 漸近的方法 (共立出版, 1961).] [Amazon]
[cited in page: 49]
T. Bohr, M. H. Jensen, G. Paladin, and A. Vulpiani,
Dynamical Systems Approach to Turbulence
(Cambridge University Press, Cambridge, 2005). [Amazon]
[cited in pages: 73, 110, 113]
G. Bordyugov, A. Pikovsky, and M. Rosenblum,
Self-emerging and turbulent chimeras in oscillator chains,
Phys. Rev. E 82, 035205(R) (2010). [Journal] [arXiv]
[cited in page: 265]
E. Brown, J. Moehlis, and P. Holmes,
On the phase reduction and response dynamics of neural oscillator populations,
Neural Comput. 16, 673 (2004). [Journal]
[cited in page: 150]
J. Buck and E. Buck,
Mechanism of rhythmic synchronous flashing of fireflies,
Science 159, 1319 (1968). [Journal]
[cited in page: 9]
J. M. Burgers,
The Non-Linear Diffusion Equation: Asymptotic Solutions and Statistical Problems
(Reidel, Dordrecht, 1974). [Amazon]
[cited in page: 85]
J. Burguete, H. Chate, F. Daviaud, and N. Mukolobwiez,
Bekki-Nozaki amplitude holes in hydrothermal nonlinear waves,
Phys. Rev. Lett. 82, 3252 (1999). [Journal] [arXiv]
[cited in page: 109]
V. Castets, E. Dulos, J. Boissonade, and P. De Kepper,
Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern,
Phys. Rev. Lett. 64, 2953 (1990). [Journal]
[cited in page: 22]
M.-L. Chabanol, V. Hakim, and W.-J. Rappel,
Collective chaos and noise in the globally coupled complex Ginzburg-Landau equation,
Physica D 103, 273 (1997). [Journal]
[cited in page: 229]
H. Chate and P. Manneville,
Stability of the Bekki-Nozaki hole solutions to the one-dimensional complex Ginzburg-Landau equation,
Phys. Lett. A 171, 183 (1992). [Journal]
[cited in page: 108]
H. Chate,
Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation,
Nonlinearity 7, 185 (1994). [Journal]
[cited in page: 116]
H. Chate and P. Manneville,
Phase diagram of the two-dimensional complex Ginzburg-Landau equation,
Physica A 224, 348 (1996). [Journal] [arXiv]
[cited in page: 105]
L.-Y. Chen, N. Goldenfeld, and Y. Oono,
Renormalization group theory for global asymptotic analysis,
Phys. Rev. Lett. 73, 1311 (1994). [Journal] [arXiv]
[cited in page: 37]
L.-Y. Chen, N. Goldenfeld, and Y. Oono,
Renormalization group and singular perturbations:
Multiple scales, boundary layers, and reductive perturbation theory,
Phys. Rev. E 54, 376 (1996). [Journal] [arXiv]
[cited in page: 37]
H. Chiba and I. Nishikawa,
Center manifold reduction for large populations of globally coupled phase oscillators,
Chaos 21, 043103 (2011). [Journal] [arXiv]
[cited in page: 257]
H. Chiba,
A proof of the Kuramoto conjecture for a bifurcation structure of the infinite dimensional Kuramoto model,
Ergodic Theory and Dynamical Systems 35, 762 (2015). [Journal] [arXiv] [RIMS]
[cited in page: 251]
H. Chiba,
A center manifold reduction of the Kuramoto-Daido model with a phase-lag,
arXiv:1609.04126 (2016). [arXiv]
[cited in page: 257]
L. M. Childs and S. H. Strogatz,
Stability diagram for the forced Kuramoto model,
Chaos 18, 043128 (2008). [Journal] [arXiv]
[cited in page: 284]
E. A. Coddington and N. Levinson,
Theory of Ordinary Differential Equations
(McGraw-Hill, New York, 1955). [Amazon]
[cited in page: 129]
P. Coullet, J. Lega, B. Houchmanzadeh, and J. Lajzerowicz,
Breaking chirality in nonequilibrium systems,
Phys. Rev. Lett. 65, 1352 (1990). [Journal]
[cited in pages: 117, 124]
P. Coullet and K. Emilsson,
Pattern formation in the strong resonant forcing of spatially distributed oscillators,
Physica A 188, 190 (1992). [Journal]
[cited in pages: 71, 117(2), 126]
P. Coullet and K. Emilsson,
Strong resonances of spatially distributed oscillators:
a laboratory to study patterns and defects,
Physica D 61, 119 (1992). [Journal]
[cited in pages: 71, 117(2)]
J. D. Crawford,
Introduction to bifurcation theory,
Rev. Mod. Phys. 63, 991 (1991). [Journal]
[cited in page: 36]
J. D. Crawford,
Amplitude expansions for instabilities in populations of globally-coupled oscillators,
J. Stat. Phys. 74, 1047 (1994). [Journal]
[cited in page: 281]
J. D. Crawford,
Scaling and singularities in the entrainment of globally coupled oscillators,
Phys. Rev. Lett. 74, 4341 (1995). [Journal]
[cited in page: 255]
J. D. Crawford and K. T. R. Davies,
Synchronization of globally coupled phase oscillators:
singularities and scaling for general couplings,
Physica D 125, 1 (1999). [Journal]
[cited in page: 255]
M. C. Cross and P. C. Hohenberg,
Pattern formation outside of equilibrium,
Rev. Mod. Phys. 65, 851 (1993). [Journal] [Amazon]
[cited in page: 110]
C. A. Czeisler, R. E. Kronauer, J. S. Allan, J. F. Duffy, M. E. Jewett, E. N. Brown, and J. M. Ronda,
Bright light induction of strong (type 0) resetting of the human circadian pacemaker,
Science 244, 1328 (1989). [Journal]
[cited in page: 145]
H. Daido,
Lower critical dimension for populations of oscillators with randomly distributed frequencies:
A renormalization-group analysis,
Phys. Rev. Lett. 61, 231 (1988). [Journal]
[cited in page: 258]
H. Daido,
Order function and macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators,
Prog. Theor. Phys. 88, 1213 (1992). [Journal]
[cited in page: 254]
H. Daido,
Generic scaling at the onset of macroscopic mutual entrainment in limit-cycle oscillators with uniform all-to-all coupling,
Phys. Rev. Lett. 73, 760 (1994). [Journal]
[cited in page: 254]
H. Daido,
Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions:
bifurcation of the order function,
Physica D 91, 24 (1996). [Journal]
[cited in page: 254]
T. Danino, O. Mondragon-Palomino, L. Tsimring, and J. Hasty,
A synchronized quorum of genetic clocks,
Nature 463, 326 (2010). [Journal]
[cited in page: 9]
S. Dano, P. G. Sorensen, and F. Hynne,
Sustained oscillations in living cells,
Nature 402, 320 (1999). [Journal]
[cited in pages: 10, 11]
P. De Kepper, V. Castets, E. Dulos, and J. Boissonade,
Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction,
Physica D 49, 161 (1991). [Journal]
[cited in page: 22]
S. De Monte, F. d'Ovidio, S. Dano, and P. G. Sorensen,
Dynamical quorum sensing: Population density encoded in cellular dynamics,
Proc. Natl. Acad. Sci. USA 104, 18377 (2007). [Journal]
[cited in page: 11]
H. Dietert,
Stability and bifurcation for the Kuramoto model,
Journal de Mathematiques Pures et Appliquees 105, 451 (2016). [Journal] [arXiv]
[cited in page: 251]
R. Dilao,
Antiphase and in-phase synchronization of nonlinear oscillators:
The Huygens's clock system,
Chaos 19, 023118 (2009). [Journal]
[cited in page: 6]
R. Dodla and C. J. Wilson,
Asynchronous response of coupled pacemaker neurons,
Phys. Rev. Lett. 102, 068102 (2009). [Journal] [arXiv]
[cited in page: 196]
B. Eckhardt, E. Ott, S. H. Strogatz, D. M. Abrams, and A. McRobie,
Modeling walker synchronization on the Millennium Bridge,
Phys. Rev. E 75, 021110 (2007). [Journal]
[cited in pages: 10, 206, 245, 284]
D. A. Egolf and H. S. Greenside,
Characterization of the transition from defect to phase turbulence,
Phys. Rev. Lett. 74, 1751 (1995). [Journal]
[cited in page: 115]
S.-I. Ei, K. Fujii, and T. Kunihiro,
Renormalization group method for reduction of evolution equations:
Invariant manifolds and envelopes,
Ann. Phys. 280, 236 (2000). [Journal] [arXiv]
[cited in page: 37]
M. B. Elowitz and S. Leibler,
A synthetic oscillatory network of transcriptional regulators,
Nature 403, 335 (2000). [Journal]
[cited in pages: 4, 9]
G. B. Ermentrout and N. Kopell,
Multiple pulse interactions and averaging in systems of coupled neural oscillators,
J. Math. Biol. 29, 195 (1991). [Journal]
[cited in pages: 139, 174]
G. B. Ermentrout,
Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators,
SIAM J. Appl. Math. 52, 1665 (1992). [Journal]
[cited in page: 312]
G. B. Ermentrout,
Type I membranes, phase resetting curves, and synchrony,
Neural Comput. 8, 979 (1996). [Journal] [XPPAUT]
[cited in pages: 147, 150, 151]
G. B. Ermentrout, R. F. Galan, and N. N. Urban,
Relating neural dynamics to neural coding,
Phys. Rev. Lett. 99, 248103 (2007). [Journal] [arXiv]
[cited in page: 150]
G. B. Ermentrout, R. F. Galan, and N. N. Urban,
Reliability, synchrony and noise,
Trends Neurosci. 31, 428 (2008). [Journal]
[cited in pages: 16, 195]
G. B. Ermentrout and D. H. Terman,
Mathematical Foundations of Neuroscience
(Springer, New York, 2010). [Amazon]
[cited in page: 151]
B. Fernandez, D. Gerard-Varet, and G. Giacomi,
Landau damping in the Kuramoto model,
Annales Henri Poincare 17, 1793 (2016). [Journal] [arXiv]
[cited in page: 251]
R. J. Field, E. Koros, and R. M. Noyes,
Oscillations in chemical systems.
II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system,
J. Am. Chem. Soc. 94, 8649 (1972). [Journal]
[cited in page: 19]
R. FitzHugh,
Impulses and physiological states in theoretical models of nerve membrane,
Biophys. J. 1, 445 (1961). [Journal]
[cited in pages: 18, 19]
P. Foerster, S. C. Muller, and B. Hess,
Curvature and spiral geometry in aggregation patterns of Dictyostelium discoideum,
Development 109, 11 (1990). [Journal]
[cited in page: 31]
H. Fukuda, N. Nakamichi, M. Hisatsune, H. Murase, and T. Mizuno,
Synchronization of plant circadian oscillators with a phase delay effect of the vein network,
Phys. Rev. Lett. 99, 098102 (2007). [Journal]
[cited in page: 14]
H. Fukuda, I. T. Tokuda, S. Hashimoto, and N. Hayasaka,
Quantitative analysis of phase wave of gene expression in the mammalian central circadian clock network,
PLoS ONE 6, e23568 (2011). [Journal]
[cited in page: 14]
H. Fukuda, K. Ukai, and T. Oyama,
Self-arrangement of cellular circadian rhythms through phase-resetting in plant roots,
Phys. Rev. E 86, 041917 (2012). [Journal]
[cited in page: 14]
H. Fukuda, H. Murase, and I. T. Tokuda,
Controlling circadian rhythms by dark-pulse perturbations in arabidopsis thaliana,
Sci. Rep. 3, 1533 (2013). [Journal]
[cited in page: 14]
T. Funato, Y. Yamamoto, S. Aoi, T. Imai, T. Aoyagi, N. Tomita, and K. Tsuchiya,
Evaluation of the phase-dependent rhythm control of human walking using phase response curves,
PLoS Comput. Biol. 12, e1004950 (2016). [Journal]
[cited in page: 32]
R. F. Galan, G. B. Ermentrout, and N. N. Urban,
Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling,
Phys. Rev. Lett. 94, 158101 (2005). [Journal]
[cited in page: 145]
J. M. Gambaudo,
Perturbation of a Hopf bifurcation by an external time-periodic forcing,
J. Diff. Eq. 57, 172 (1985). [Journal]
[cited in page: 71]
D. Garcia-Alvarez, A. Bahraminasab, A. Stefanovska, and P. V. E. McClintock,
Competition between noise and coupling in the induction of synchronisation,
Eur. Phys. Lett. 88, 30005 (2009). [Journal] [arXiv]
[cited in page: 196]
V. Garcia-Morales and K. Krischer,
The complex Ginzburg-Landau equation: an introduction,
Contemporary Physics 53, 79 (2012). [Journal]
[cited in page: 73]
C. W. Gardiner,
Handbook of Stochastic Methods:
For Physics, Chemistry and the Natural Sciences
(Springer, Berlin, 1997). [Amazon]
[cited in page: 181]
L. Gil,
Space and time intermittency behavior of a one-dimensional complex Ginzburg-Landau equation,
Nonlinearity 4, 1213 (1991). [Journal]
[cited in page: 116]
P. Glansdorff and I. Prigogine,
Thermodynamic Theory of Structure, Stability and Fluctuations
(Wiley, London, 1971). [Amazon]
[松本元・竹山協三 訳: 構造・安定性・ゆらぎ - その熱力学的理論 (みすず書房, 1977).] [Amazon]
[cited in page: 3]
C. J. Goebel,
Comment on "Constants of motion for superconductor arrays",
Physica D 80, 18 (1995). [Journal]
[cited in page: 211]
D. S. Goldobin and A. Pikovsky,
Synchronization of self-sustained oscillators by common white noise,
Physica A 351, 126 (2005). [Journal]
[cited in page: 192]
D. S. Goldobin and A. Pikovsky,
Synchronization and desynchronization of self-sustained oscillators by common noise,
Phys. Rev. E 71, 045201 (2005). [Journal]
[cited in pages: 195, 196]
D. S. Goldobin, J. N. Teramae, H. Nakao, and G. B. Ermentrout,
Dynamics of limit-cycle oscillators subject to general noise,
Phys. Rev. Lett. 105, 154101 (2010). [Journal] [arXiv]
[cited in pages: 181, 192]
P. Grassberger and I. Procaccia,
Measuring the strangeness of strange attractors,
Physica D 9, 189 (1983). [Journal]
[cited in page: 115]
T. Gregor, K. Fujimoto, N. Masaki, and S. Sawai,
The onset of collective behavior in social amoebae,
Science 328, 1021 (2010). [Journal]
[cited in page: 10]
J. Guckenheimer,
Isochrons and phaseless sets,
J. Math. Biol. 1, 259 (1975). [Journal]
[cited in page: 132]
J. Guckenheimer and P. Holmes,
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
(Springer, Berlin, 1983). [Amazon]
[cited in pages: 3, 36]
B. Gutkin, G. B. Ermentrout, and M. Rudolph,
Spike generating dynamics and the conditions for spike-time precision in cortical neurons,
J. Comput. Neurosci. 15, 91 (2003). [Journal]
[cited in page: 192]
P. Hadley and M. R. Beasley,
Dynamical states and stability of linear arrays of Josephson junctions,
Appl. Phys. Lett. 50, 621 (1987). [Journal]
[cited in page: 26]
P. S. Hagan,
Spiral waves in reaction-diffusion equations,
SIAM J. Appl. Math. 42, 762 (1982). [Journal]
[cited in page: 102]
D. Haim, O. Lev, L. M. Pismen, and M. Sheintuch,
Modeling periodic and chaotic dynamics in anodic nickel dissolution,
J. Phys. Chem. 96, 2676 (1992). [Journal]
[cited in page: 31]
V. Hakim and W.-J. Rappel,
Dynamics of the globally coupled complex Ginzburg-Landau equation,
Phys. Rev. A 46, R7347 (1992). [Journal]
[cited in page: 229]
C. Hammond, H. Bergman, and P. Brown,
Pathological synchronization in Parkinson's disease:
networks, models and treatments,
Trends Neurosci. 30, 357 (2007). [Journal]
[cited in page: 9]
S. K. Han, C. Kurrer, and Y. Kuramoto,
Dephasing and bursting in coupled neural oscillators,
Phys. Rev. Lett. 75, 3190 (1995). [Journal]
[cited in page: 229]
D. Hansel, G. Mato, and C. Meunier,
Clustering and slow switching in globally coupled phase oscillators,
Phys. Rev. E 48, 3470 (1993). [Journal]
[cited in pages: 217, 225]
D. Hansel, G. Mato, and C. Meunier,
Synchrony in excitatory neural networks,
Neural Comput. 7, 307 (1995). [Journal]
[cited in page: 161]
T. Harada, H. Tanaka, M. J. Hankins, and I. Z. Kiss,
Optimal waveform for the entrainment of a weakly forced oscillator,
Phys. Rev. Lett. 105, 088301 (2010). [Journal] [arXiv]
[cited in page: 155]
A. L. Hodgkin and A. F. Huxley,
A quantitative description of membrane current and its application to conduction and excitation in nerve,
J. Physiol. 117, 500 (1952). [Journal1] [Journal2]
[cited in page: 19]
H. Hong, H. Park, and M. Y. Choi,
Collective phase synchronization in locally-coupled limit-cycle oscillators,
Phys. Rev. E 70, 045204 (2004). [Journal] [arXiv]
[cited in page: 258]
H. Hong, H. Park, and M. Y. Choi,
Collective synchronization in spatially extended systems of coupled oscillators with random frequencies,
Phys. Rev. E 72, 036217 (2005). [Journal] [arXiv]
[cited in page: 258]
H. Hong, M. Ha, and H. Park,
Finite-size scaling in complex networks,
Phys. Rev. Lett. 98, 258701 (2007). [Journal] [arXiv]
[cited in page: 258]
H. Hong, H. Chate, H. Park, and L.-H. Tang,
Entrainment transition in populations of random frequency oscillators,
Phys. Rev. Lett. 99, 184101 (2007). [Journal] [arXiv]
[cited in page: 258]
H. Hong and S. H. Strogatz,
Kuramoto model of coupled oscillators with positive and negative coupling parameters:
An example of conformist and contrarian oscillators,
Phys. Rev. Lett. 106, 054102 (2011). [Journal]
[cited in page: 284]
H. Hong and S. H. Strogatz,
Conformists and contrarians in a Kuramoto model with identical natural frequencies,
Phys. Rev. E 84, 046202 (2011). [Journal] [arXiv]
[cited in page: 284]
H. Hong and S. H. Strogatz,
Mean-field behavior in coupled oscillators with attractive and repulsive interactions,
Phys. Rev. E 85, 056210 (2012). [Journal]
[cited in page: 284]
F. C. Hoppensteadt and E. M. Izhikevich,
Weakly Connected Neural Networks
(Springer, New York, 1997). [Amazon]
[cited in pages: 151, 174]
J. M. Hyman and B. Nicolaenko,
The Kuramoto-Sivashinsky equation:
A bridge between PDE's and dynamical systems,
Physica D 18, 113 (1986). [Journal]
[cited in page: 110]
T. Ichinomiya,
Frequency synchronization in random oscillator network,
Phys. Rev. E 70, 026116 (2004). [Journal] [arXiv]
[cited in page: 258]
R. Imbihl and G. Ertl,
Oscillatory kinetics in heterogeneous catalysis,
Chem. Rev. 95, 697 (1995). [Journal] [Nobel]
[cited in page: 89]
M. Ipsen, L. Kramer, and P. G. Sorensen,
Amplitude equations for description of chemical reaction diffusion systems,
Phys. Rep. 337, 193 (2000). [Journal]
[cited in page: 73]
E. M. Izhikevich,
Dynamical Systems in Neuroscience:
The Geometry of Excitability and Bursting
(MIT Press, Cambridge, MA, 2007). [Amazon] [Scholarpedia]
[cited in pages: 139, 151]
S. Jakubith, H. H. Rotermund, W. Engel, A. von Oertzen, and G. Ertl,
Spatiotemporal concentration patterns in a surface reaction:
Propagating and standing waves, rotating spirals, and turbulence,
Phys. Rev. Lett. 65, 3013 (1990). [Journal]
[cited in page: 89]
J. Javaloyes, M. Perrin, and A. Politi,
Collective atomic recoil laser as a synchronization transition,
Phys. Rev. E 78, 011108 (2008). [Journal] [arXiv]
[cited in page: 12]
R. V. Jensen,
Synchronization of randomly driven nonlinear oscillators,
Phys. Rev. E 58, R6907 (1998). [Journal]
[cited in page: 192]
B. D. Josephson,
Possible new effects in superconductive tunnelling,
Phys. Lett. 1, 251 (1962). [Journal]
[cited in page: 25]
K. Kamino, K. Fujimoto, and S. Sawai,
The collective oscillations in developing cells: Insights from simple systems,
Dev. Growth Diff. 53, 503 (2011). [Journal]
[cited in page: 10]
K. Kaneko,
Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements,
Physica D 41, 137 (1990). [Journal]
[cited in page: 218]
T. Kano and S. Kinoshita,
Method to control the coupling function using multilinear feedback,
Phys. Rev. E 78, 056210 (2008). [Journal]
[cited in page: 226]
M. Kapitaniak, K. Czolczynski, P. Perlikowski, A. Stefanski, and T. Kapitaniak,
Synchronization of clocks,
Phys. Rep. 517, 1 (2012). [Journal]
[cited in page: 6]
Y. Kawamura and Y. Kuramoto,
Onset of collective oscillation in chemical turbulence under global feedback,
Phys. Rev. E 69, 016202 (2004). [Journal] [arXiv] [PTPS]
[cited in pages: 67, 294]
Y. Kawamura, H. Nakao, and Y. Kuramoto,
Noise-induced turbulence in nonlocally coupled oscillators,
Phys. Rev. E 75, 036209 (2007). [Journal] [arXiv] [NCTAM]
[cited in pages: 288, 297, 304, 307]
Y. Kawamura,
Chimera Ising walls in forced nonlocally coupled oscillators,
Phys. Rev. E 75, 056204 (2007). [Journal] [arXiv]
[cited in page: 271]
Y. Kawamura,
Hole structures in nonlocally coupled noisy phase oscillators,
Phys. Rev. E 76, 047201 (2007). [Journal] [arXiv]
[cited in pages: 288, 295(2)]
Y. Kawamura, H. Nakao, K. Arai, H. Kori, and Y. Kuramoto,
Collective phase sensitivity,
Phys. Rev. Lett. 101, 024101 (2008). [Journal] [arXiv]
[cited in pages: 309, 311]
Y. Kawamura, H. Nakao, K. Arai, H. Kori, and Y. Kuramoto,
Phase synchronization between collective rhythms of globally coupled oscillator groups:
Noisy identical case,
Chaos 20, 043109 (2010). [Journal] [arXiv]
[cited in page: 311]
Y. Kawamura, H. Nakao, K. Arai, H. Kori, and Y. Kuramoto,
Phase synchronization between collective rhythms of globally coupled oscillator groups:
Noiseless non-identical case,
Chaos 20, 043110 (2010). [Journal] [arXiv]
[cited in pages: 245, 313]
Y. Kawamura, H. Nakao, and Y. Kuramoto,
Collective phase description of globally coupled excitable elements,
Phys. Rev. E 84, 046211 (2011). [Journal] [arXiv]
[cited in page: 319]
Y. Kawamura and H. Nakao,
Collective phase description of oscillatory convection,
Chaos 23, 043129 (2013). [Journal] [arXiv]
[cited in page: 319]
Y. Kawamura and H. Nakao,
Noise-induced synchronization of oscillatory convection and its optimization,
Phys. Rev. E 89, 012912 (2014). [Journal] [arXiv]
[cited in page: 319]
Y. Kawamura,
From the Kuramoto-Sakaguchi model to the Kuramoto-Sivashinsky equation,
Phys. Rev. E 89, 010901(R) (2014). [Journal] [arXiv]
[cited in pages: 297, 304, 309]
Y. Kawamura,
Collective phase dynamics of globally coupled oscillators:
Noise-induced anti-phase synchronization,
Physica D 270, 20 (2014). [Journal] [arXiv] [RIMS]
[cited in page: 311]
Y. Kawamura,
Phase synchronization between collective rhythms of fully locked oscillator groups,
Sci. Rep. 4, 4832 (2014). [Journal] [arXiv]
[cited in page: 317]
Y. Kawamura and H. Nakao,
Phase description of oscillatory convection with a spatially translational mode,
Physica D 295-296, 11 (2015). [Journal] [arXiv]
[cited in page: 319]
Y. Kawamura and H. Nakao,
Optimization of noise-induced synchronization of oscillator networks,
Phys. Rev. E 94, 032201 (2016). [Journal]
[cited in page: 317]
S. B. S. Khalsa, M. E. Jewett, C. Cajochen, and C. A. Czeisler,
A phase response curve to single bright light pulses in human subjects,
J. Physiol. 549, 945 (2003). [Journal]
[cited in page: 145]
M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl,
Controlling chemical turbulence by global delayed feedback:
pattern formation in catalytic CO oxidation on Pt(110),
Science 292, 1357 (2001). [Journal]
[cited in pages: 66, 89]
I. Z. Kiss, Y. Zhai, and J. L. Hudson,
Emerging coherence in a population of chemical oscillators,
Science 296, 1676 (2002). [Journal]
[cited in pages: 12, 13, 245]
I. Z. Kiss and J. L. Hudson,
Noise-aided synchronization of coupled chaotic electrochemical oscillators,
Phys. Rev. E 70, 026210 (2004). [Journal]
[cited in page: 196]
I. Z. Kiss, Y. Zhai, and J. L. Hudson,
Predicting mutual entrainment of oscillators with experiment-based phase models,
Phys. Rev. Lett. 94, 248301 (2005). [Journal]
[cited in page: 168]
I. Z. Kiss, C. G. Rusin, H. Kori, and J. L. Hudson,
Engineering complex dynamical structures:
sequential patterns and desynchronization,
Science 316, 1886 (2007). [Journal]
[cited in pages: 12, 31, 66, 216, 226]
H. Kitahata, J. Taguchi, M. Nagayama, T. Sakurai, Y. Ikura, A. Osa, Y. Sumino, M. Tanaka, E. Yokoyama, and H. Miike,
Oscillation and synchronization in the combustion of candles,
J. Phys. Chem. A 113, 8164 (2009). [Journal] [YouTube]
[cited in page: 6]
T.-W. Ko and G. B. Ermentrout,
Partially locked states in coupled oscillators due to inhomogeneous coupling,
Phys. Rev. E 78, 016203 (2008). [Journal] [arXiv]
[cited in page: 258]
M. U. Kobayashi and T. Mizuguchi,
Chaotically oscillating interfaces in a parametrically forced system,
Phys. Rev. E 73, 016212 (2006). [Journal]
[cited in page: 124]
Y. Kobayashi and H. Kori,
Design principle of multi-cluster and desynchronized states in oscillatory media via nonlinear global feedback,
New J. Phys. 11, 033018 (2009). [Journal] [arXiv]
[cited in page: 272]
M. I. Kohira, H. Kitahata, N. Magome, and K. Yoshikawa,
Plastic bottle oscillator as an on-off-type oscillator:
Experiments, modeling, and stability analyses of single and coupled systems,
Phys. Rev. E 85, 026204 (2012). [Journal]
[cited in page: 6]
N. Kopell and L. N. Howard,
Plane wave solutions to reaction-diffusion equations,
Stud. Appl. Math. 52, 291 (1973). [Journal]
[cited in page: 79]
H. Kori and Y. Kuramoto,
Slow switching in globally coupled oscillators:
robustness and occurrence through delayed coupling,
Phys. Rev. E 63, 046214 (2001). [Journal] [arXiv]
[cited in pages: 217, 224, 225(2)]
H. Kori,
Slow switching in a population of delayed pulse-coupled oscillators,
Phys. Rev. E 68, 021919 (2003). [Journal] [arXiv]
[cited in pages: 171, 217, 225]
H. Kori and A. S. Mikhailov,
Entrainment of randomly coupled oscillator networks by a pacemaker,
Phys. Rev. Lett. 93, 254101 (2004). [Journal] [arXiv]
[cited in page: 258]
H. Kori and A. S. Mikhailov,
Strong effects of network architecture in the entrainment of coupled oscillator systems,
Phys. Rev. E 74, 066115 (2006). [Journal] [arXiv]
[cited in page: 258]
H. Kori, C. G. Rusin, I. Z. Kiss, and J. L. Hudson,
Synchronization engineering:
Theoretical framework and application to dynamical clustering,
Chaos 18, 026111 (2008). [Journal] [arXiv]
[cited in pages: 31, 216, 226]
H. Kori, Y. Kawamura, H. Nakao, K. Arai, and Y. Kuramoto,
Collective-phase description of coupled oscillators with general network structure,
Phys. Rev. E 80, 036207 (2009). [Journal] [arXiv]
[cited in pages: 311, 317, 318, 319]
郡宏・森田善久,
生物リズムと力学系
(共立出版, 2011). [Amazon] [YouTube]
[cited in page: 3]
H. Kori, Y. Kuramoto, S. Jain, I. Z. Kiss, and J. L. Hudson,
Clustering in globally coupled oscillators near a Hopf bifurcation: Theory and experiments,
Phys. Rev. E 89, 062906 (2014). [Journal] [arXiv]
[cited in page: 67]
K. Kotani, I. Yamaguchi, Y. Ogawa, Y. Jimbo, H. Nakao, and G. B. Ermentrout,
Adjoint method provides phase response functions for delay-induced oscillations,
Phys. Rev. Lett. 109, 044101 (2012). [Journal]
[cited in page: 204]
S. Yu. Kourtchatov, V. V. Likhanskii, A. P. Napartovich, F. T. Arecchi, and A. Lapucci,
Theory of phase locking of globally coupled laser arrays,
Phys. Rev. A 52, 4089 (1995). [Journal]
[cited in page: 12]
G. Kozyreff, A. G. Vladimirov, and P. Mandel,
Global coupling with time delay in an array of semiconductor lasers,
Phys. Rev. Lett. 85, 3809 (2000). [Journal]
[cited in page: 12]
G. Kozyreff, A. G. Vladimirov, and P. Mandel,
Dynamics of a semiconductor laser array with delayed global coupling,
Phys. Rev. E 64, 016613 (2001). [Journal]
[cited in page: 12]
B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, and R. Mrowka,
Uncovering interaction of coupled oscillators from data,
Phys. Rev. E 76, 055201(R) (2007). [Journal]
[cited in page: 168]
B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, and R. Mrowka,
Phase dynamics of coupled oscillators reconstructed from data,
Phys. Rev. E 77, 066205 (2008). [Journal]
[cited in page: 168]
B. Kralemann, A. Pikovsky, and M. Rosenblum,
Reconstructing phase dynamics of oscillator networks,
Chaos 21, 025104 (2011). [Journal] [arXiv]
[cited in page: 168]
B. Kralemann, M. Fruhwirth, A. Pikovsky, M. Rosenblum, T. Kenner, J. Schaefer, and M. Moser,
In vivo cardiac phase response curve elucidates human respiratory heart rate variability,
Nature Communications 4, 2418 (2013). [Journal]
[cited in page: 168]
R. Kubo, M. Toda, and N. Hashitsume,
Statistical Physics II: Nonequilibrium Statistical Mechanics
(Springer, Berlin, 1985). [Amazon]
[cited in page: 181]
L. Kuhnert,
A new optical photochemical memory device in a light-sensitive chemical active medium,
Nature 319, 393 (1986). [Journal]
[cited in page: 21]
Y. Kuramoto and T. Tsuzuki,
Reductive perturbation approach to chemical instabilities,
Prog. Theor. Phys. 52, 1399 (1974). [Journal]
[cited in pages: 23, 36, 64]
Y. Kuramoto and T. Tsuzuki,
On the formation of dissipative structures in reaction-diffusion systems
- reductive perturbation approach -,
Prog. Theor. Phys. 54, 687 (1975). [Journal]
[cited in page: 64]
Y. Kuramoto,
Self-entrainment of a population of coupled non-linear oscillators,
in International Symposium on Mathematical Problems in Theoretical Physics, edited by H. Araki,
Lecture Notes in Physics Vol. 39 (Springer, Berlin, 1975) p. 420. [Journal] [CiNii] [YouTube]
[cited in page: 232]
Y. Kuramoto and T. Tsuzuki,
Persistent propagation of concentration waves in dissipative media far from thermal equilibrium,
Prog. Theor. Phys. 55, 356 (1976). [Journal]
[cited in pages: 83, 89]
Y. Kuramoto and T. Yamada,
Turbulent state in chemical reactions,
Prog. Theor. Phys. 56, 679 (1976). [Journal]
[cited in page: 89]
Y. Kuramoto and T. Yamada,
Pattern formation in oscillatory chemical reactions,
Prog. Theor. Phys. 56, 724 (1976). [Journal]
[cited in page: 92]
Y. Kuramoto,
Diffusion-induced chaos in reaction systems,
Prog. Theor. Phys. Suppl. 64, 346 (1978). [Journal]
[cited in page: 89]
Y. Kuramoto and S. Koga,
Turbulized rotating chemical waves,
Prog. Theor. Phys. 66, 1081 (1981). [Journal]
[cited in page: 105]
Y. Kuramoto,
Chemical Oscillations, Waves, and Turbulence
(Springer, New York, 1984; Dover, New York, 2003). [Amazon]
[cited in pages: 35, 92, 138, 139, 174, 197, 232(2), 281, 285]
Y. Kuramoto,
Phase dynamics of weakly unstable periodic structures,
Prog. Theor. Phys. 71, 1182 (1984). [Journal]
[cited in page: 86]
蔵本由紀,
動的縮約の構造,
物性研究 49, 299 (1987). [CiNii] [PTPS]
[cited in page: 41]
Y. Kuramoto and I. Nishikawa,
Onset of collective rhythms in large population of coupled oscillators,
in Cooperative Dynamics in Complex Physical Systems, edited by H. Takayama,
(Springer, Berlin, 1989) p. 300. [Amazon]
[cited in page: 252]
Y. Kuramoto,
Collective synchronization of pulse-coupled oscillators and excitable units,
Physica D 50, 15 (1991). [Journal]
[cited in page: 171]
Y. Kuramoto,
Scaling behavior of turbulent oscillators with non-local interaction,
Prog. Theor. Phys. 94, 321 (1995). [Journal]
[cited in pages: 68, 265]
Y. Kuramoto and D. Battogtokh,
Coexistence of coherence and incoherence in nonlocally coupled phase oscillators,
Nonlinear Phenom. Complex Syst. 5, 380 (2002). [Journal] [arXiv]
[cited in pages: 259, 261]
蔵本由紀 編,
リズム現象の世界
(東京大学出版会, 2005). [Amazon]
[cited in page: 5]
蔵本由紀,
非線形科学 同期する世界
(集英社新書, 2011). [Amazon]
[cited in page: 3]
W. Kurebayashi, K. Fujiwara, and T. Ikeguchi,
Colored noise induces synchronization of limit cycle oscillators,
Eur. Phys. Lett. 97, 50009 (2012). [Journal] [arXiv]
[cited in page: 195]
W. Kurebayashi, S. Shirasaka, and H. Nakao,
Phase reduction method for strongly perturbed limit cycle oscillators,
Phys. Rev. Lett. 111, 214101 (2013). [Journal] [arXiv]
[cited in page: 204]
C. R. Laing,
Chimera states in heterogeneous networks,
Chaos 19, 013113 (2009). [Journal] [arXiv]
[cited in pages: 283, 317]
C. R. Laing,
The dynamics of chimera states in heterogeneous Kuramoto networks,
Physica D 238, 1569 (2009). [Journal]
[cited in pages: 297, 317]
C. R. Laing,
Derivation of a neural field model from a network of theta neurons,
Phys. Rev. E 90, 010901(R) (2014). [Journal]
[cited in page: 285]
L. D. Landau,
On the problem of turbulence,
C. R. Dokl. Acad. Sci. URSS 44, 31 (1944). [Amazon]
[cited in page: 60]
L. D. Landau,
On the vibrations of the electronic plasma,
J. Phys. USSR 10, 25 (1946). [Amazon]
[cited in page: 253]
W. S. Lee, E. Ott, and T. M. Antonsen,
Large coupled oscillator systems with heterogeneous interaction delays,
Phys. Rev. Lett. 103, 044101 (2009). [Journal] [arXiv]
[cited in page: 284]
W. S. Lee, J. G. Restrepo, E. Ott, and T. M. Antonsen,
Dynamics and pattern formation in large systems of spatially-coupled oscillators with finite response times,
Chaos 21, 023122 (2011). [Journal] [arXiv]
[cited in page: 297]
J. Lega, B. Janiaud, S. Jucquois, and V. Croquette,
Localized phase jumps in wave trains,
Phys. Rev. A 45, 5596 (1992). [Journal]
[cited in page: 109]
I. Lengyel and I. R. Epstein,
Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system,
Science 251, 650 (1991). [Journal]
[cited in page: 22]
K. K. Lin, E. Shea-Brown, and L.-S. Young,
Spike-time reliability of layered neural oscillator networks,
J. Comput. Neurosci. 27, 135 (2009). [Journal] [arXiv]
[cited in page: 196]
K. K. Lin, E. Shea-Brown, and L.-S. Young,
Reliability of coupled oscillators,
J. Nonlinear Sci. 19, 497 (2009). [Journal] [arXiv1] [arXiv2]
[cited in page: 196]
Z. Lu, K. Klein-Cardena, S. Lee, T. M. Antonsen, M. Girvan, and E. Ott,
Resynchronization of circadian oscillators and the east-west asymmetry of jet-lag,
Chaos 26, 094811 (2016). [Journal]
[cited in page: 284]
T. B. Luke, E. Barreto, and P. So,
Complete classification of the macroscopic behavior of a heterogeneous network of theta neurons,
Neural Comput. 25, 3207 (2013). [Journal]
[cited in page: 285]
T. B. Luke, E. Barreto, and P. So,
Macroscopic complexity from an autonomous network of networks of theta neurons,
Front. Comput. Neurosci. 8, 145 (2014). [Journal]
[cited in page: 285]
Z. F. Mainen and T. J. Sejnowski,
Reliability of spike timing in neocortical neurons,
Science 268, 1503 (1995). [Journal]
[cited in pages: 14, 15, 16, 192]
I. G. Malkin,
Methods of Poincare and Liapunov in Theory of Non-Linear Oscillations (1949).
[in Russian: "Metodi Puankare i Liapunova v teorii nelineinix kolebanii", Gostexizdat, Moscow.]
[cited in page: 151]
I. G. Malkin,
Some Problems in Nonlinear Oscillation Theory (1956).
[in Russian: "Nekotorye zadachi teorii nelineinix kolebanii", Gostexizdat, Moscow.]
[cited in page: 151]
P. Manneville,
Liapounov exponents for the Kuramoto-Sivashinsky model,
in Macroscopic Modeling of Turbulent Flows and Fluid Mixtures, edited by O. Pironne,
Lecture Notes in Physics Vol. 230 (Springer, Berlin, 1985) p. 319. [Journal]
[cited in page: 113]
P. Manneville,
Dissipative Structures and Weak Turbulence
(Academic Press, Boston, 1990). [Amazon]
[cited in pages: 110, 115]
P. Manneville and H. Chate,
Phase turbulence in the two-dimensional complex Ginzburg-Landau equation,
Physica D 96, 30 (1996). [Journal]
[cited in page: 110]
J. E. Marsden and M. McCracken,
The Hopf Bifurcation and Its Applications
(Springer, New York, 1976). [Amazon]
[cited in page: 36]
E. A. Martens, E. Barreto, S. H. Strogatz, E. Ott, P. So, and T. M. Antonsen,
Exact results for the Kuramoto model with a bimodal frequency distribution,
Phys. Rev. E 79, 026204 (2009). [Journal] [arXiv]
[cited in pages: 281, 283]
E. A. Martens, C. R. Laing, and S. H. Strogatz,
Solvable model of spiral wave chimeras,
Phys. Rev. Lett. 104, 044101 (2010). [Journal] [arXiv]
[cited in page: 268]
E. A. Martens, S. Thutupalli, A. Fourriere, and O. Hallatschek,
Chimera states in mechanical oscillator networks,
Proc. Natl. Acad. Sci. USA 110, 10563 (2013). [Journal] [arXiv]
[cited in page: 272]
S. A. Marvel and S. H. Strogatz,
Invariant submanifold for series arrays of Josephson junctions,
Chaos 19, 013132 (2009). [Journal] [arXiv]
[cited in page: 213]
S. A. Marvel, R. E. Mirollo, and S. H. Strogatz,
Identical phase oscillators with global sinusoidal coupling evolve by Mobius group action,
Chaos 19, 043104 (2009). [Journal] [arXiv]
[cited in pages: 211, 213]
N. Masuda, Y. Kawamura, and H. Kori,
Analysis of relative influence of nodes in directed networks,
Phys. Rev. E 80, 046114 (2009). [Journal] [arXiv]
[cited in pages: 316, 319]
N. Masuda, Y. Kawamura, and H. Kori,
Collective fluctuations in networks of noisy components,
New J. Phys. 12, 093007 (2010). [Journal] [arXiv] [JSPE]
[cited in page: 316]
P. C. Matthews and S. M. Cox,
One-dimensional pattern formation with Galilean invariance near a stationary bifurcation,
Phys. Rev. E 62, R1473 (2000). [Journal]
[cited in page: 89]
D. M. Michelson and G. I. Sivashinsky,
Nonlinear analysis of hydrodynamic instability in laminar flames.
II. Numerical experiments,
Acta Astronautica 4, 1207 (1977). [Journal]
[cited in page: 89]
三池秀敏・森 義仁・山口智彦,
非平衡系の科学III: 反応・拡散系のダイナミクス
(講談社, 1997). [Amazon]
[cited in page: 21]
A. S. Mikhailov and K. Showalter,
Control of waves, patterns and turbulence in chemical systems,
Phys. Rep. 425, 79 (2006). [Journal]
[cited in pages: 13, 73, 117]
J. G. Milton,
Introduction to Focus Issue:
Bipedal Locomotion - From Robots to Humans,
Chaos 19, 026101 (2009) and Focus Issue Articles. [Journal]
[cited in page: 32]
R. E. Mirollo and S. H. Strogatz,
Amplitude death in an array of limit-cycle oscillators,
J. Stat. Phys. 60, 245 (1990). [Journal]
[cited in page: 248]
R. E. Mirollo and S. H. Strogatz,
The spectrum of the locked state for the Kuramoto model of coupled oscillators,
Physica D 205, 249 (2005). [Journal]
[cited in page: 312]
R. E. Mirollo and S. H. Strogatz,
The spectrum of the partially locked state for the Kuramoto model,
J. Nonlinear Sci. 17, 309 (2007). [Journal] [arXiv]
[cited in pages: 251, 313]
R. E. Mirollo,
The asymptotic behavior of the order parameter for the infinite-N Kuramoto model,
Chaos 22, 043118 (2012). [Journal]
[cited in page: 280]
T. Miyano and T. Tsutsui,
Data synchronization in a network of coupled phase oscillators,
Phys. Rev. Lett. 98, 024101 (2007). [Journal]
[cited in page: 33]
J. Miyazaki and S. Kinoshita,
Determination of a coupling function in multicoupled oscillators,
Phys. Rev. Lett. 96, 194101 (2006). [Journal]
[cited in page: 167]
J. Miyazaki and S. Kinoshita,
Method for determining a coupling function in coupled oscillators with application to Belousov-Zhabotinsky oscillators,
Phys. Rev. E 74, 056209 (2006). [Journal]
[cited in page: 167]
T. Mizuguchi and S. Sasa,
Oscillating interfaces in parametrically forced systems,
Prog. Theor. Phys. 89, 599 (1993). [Journal]
[cited in page: 124]
A. Moiseff and J. Copeland,
Firefly synchrony: a behavioral strategy to minimize visual clutter,
Science 329, 181 (2010). [Journal]
[cited in page: 9]
O. Mondragon-Palomino, T. Danino, J. Selimkhanov, L. Tsimring, and J. Hasty,
Entrainment of a population of synthetic genetic oscillators,
Science 333, 1315 (2011). [Journal]
[cited in page: 9]
E. Montbrio, J. Kurths, and B. Blasius,
Synchronization of two interacting populations of oscillators,
Phys. Rev. E 70, 056125 (2004). [Journal] [arXiv]
[cited in page: 317]
E. Montbrio, D. Pazo, and A. Roxin,
Macroscopic description for networks of spiking neurons,
Phys. Rev. X 5, 021028 (2015). [Journal] [arXiv]
[cited in page: 285]
E. Mosekilde, Y. Maistrenko, and D. Postnov,
Chaotic Synchronization: Applications to Living Systems
(World Scientific, Singapore, 2002). [Amazon]
[cited in page: 5]
A. E. Motter, S. A. Myers, M. Anghel, and T. Nishikawa,
Spontaneous synchrony in power-grid networks,
Nature Physics 9, 191 (2013). [Journal] [arXiv]
[cited in page: 32]
K. Nagai, H. Nakao, and Y. Tsubo,
Synchrony of neural oscillators induced by random telegraphic currents,
Phys. Rev. E 71, 036217 (2005). [Journal]
[cited in page: 195]
K. Nagai and H. Nakao,
Experimental synchronization of circuit oscillations induced by common telegraph noise,
Phys. Rev. E 79, 036205 (2009). [Journal] [arXiv]
[cited in page: 195]
K. H. Nagai and H. Kori,
Noise-induced synchronization of a large population of globally coupled nonidentical oscillators,
Phys. Rev. E 81, 065202(R) (2010). [Journal] [arXiv]
[cited in page: 284]
J. Nagumo, S. Arimoto, and S. Yoshizawa,
An active pulse transmission line simulating nerve axon,
Proc. IRE 50, 2061 (1962). [Journal]
[cited in page: 19]
N. Nakagawa and Y. Kuramoto,
Collective chaos in a population of globally coupled oscillators,
Prog. Theor. Phys. 89, 313 (1993). [Journal]
[cited in page: 229]
N. Nakagawa and Y. Kuramoto,
Anomalous Lyapunov spectrum in globally coupled oscillators,
Physica D 80, 307 (1995). [Journal]
[cited in page: 229]
H. Nakao, K. Arai, K. Nagai, Y. Tsubo, and Y. Kuramoto,
Synchrony of limit-cycle oscillators induced by random external impulses,
Phys. Rev. E 72, 026220 (2005). [Journal] [arXiv]
[cited in page: 195]
H. Nakao, K. Arai, and Y. Kawamura,
Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators,
Phys. Rev. Lett. 98, 184101 (2007). [Journal] [arXiv]
[cited in pages: 193, 195]
H. Nakao, J. N. Teramae, D. S. Goldobin, and Y. Kuramoto,
Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise,
Chaos 20, 033126 (2010). [Journal] [arXiv]
[cited in page: 181]
H. Nakao, T. Yanagita, and Y. Kawamura,
Phase-reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems,
Phys. Rev. X 4, 021032 (2014). [Journal] [arXiv]
[cited in page: 319]
H. Nakao,
Phase reduction approach to synchronisation of nonlinear oscillators,
Contemporary Physics 57, 188 (2016). [Journal] [arXiv]
[cited in page: 204]
Z. Neda, E. Ravasz, Y. Brechet, T. Vicsek, and A.-L. Barabasi,
Self-organizing processes: The sound of many hands clapping,
Nature 403, 849 (2000). [Journal]
[cited in page: 31]
Z. Neda, E. Ravasz, T. Vicsek, Y. Brechet, and A.-L. Barabasi,
Physics of the rhythmic applause,
Phys. Rev. E 61, 6987 (2000). [Journal]
[cited in page: 31]
A. C. Newell and J. A. Whitehead,
Finite bandwidth, finite amplitude convection,
J. Fluid Mech. 38, 279 (1969). [Journal]
[cited in page: 64]
A. C. Newell,
Envelope equations,
Lectures in Appl. Math. 15, 157 (1974). [Amazon]
[cited in page: 81]
G. Nicolis and I. Prigogine,
Self-Organization in Nonequilibrium Systems:
From Dissipative Structures to Order through Fluctuations
(Wiley, New York, 1977). [Amazon]
[小畠陽之助・相沢洋二 訳: 散逸構造 - 自己秩序形成の物理学的基礎 (岩波書店, 1980).] [Amazon]
[cited in page: 23]
西川郁子,
振動同期を用いた交通信号機制御法について,
システム/制御/情報 52, 163 (2008). [CiNii]
[cited in page: 32]
T. Nishikawa and A. E. Motter,
Synchronization is optimal in non-diagonalizable networks,
Phys. Rev. E 73, 065106(R) (2006). [Journal] [arXiv]
[cited in page: 312]
T. Nishikawa and A. E. Motter,
Maximum performance at minimum cost in network synchronization,
Physica D 224, 77 (2006). [Journal] [arXiv]
[cited in page: 312]
T. Nishikawa and A. E. Motter,
Comparative analysis of existing models for power-grid synchronization,
New J. Phys. 17, 015012 (2015). [Journal] [arXiv]
[cited in page: 32]
西浦廉政,
非平衡ダイナミクスの数理
(岩波書店, 2009). [Amazon]
[cited in page: 37]
S. Nkomo, M. R. Tinsley, and K. Showalter,
Chimera states in populations of nonlocally coupled chemical oscillators,
Phys. Rev. Lett. 110, 244102 (2013). [Journal]
[cited in page: 272]
M. Nomura, T. Fukai, and T. Aoyagi,
Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses,
Neural Comput. 15, 2179 (2003). [Journal]
[cited in page: 162]
M. Nomura and T. Aoyagi,
Stability of synchronous solutions in weakly coupled neuron networks,
Prog. Theor. Phys. 113, 911 (2005). [Journal]
[cited in page: 162]
V. Novicenko and K. Pyragas,
Phase reduction of weakly perturbed limit cycle oscillations in time-delay systems,
Physica D 241, 1090 (2012). [Journal]
[cited in page: 204]
V. Novicenko and K. Pyragas,
Phase-reduction-theory-based treatment of extended delayed feedback control algorithm in the presence of a small time delay mismatch,
Phys. Rev. E 86, 026204 (2012). [Journal]
[cited in page: 204]
K. Nozaki and Y. Oono,
Renormalization-group theoretical reduction,
Phys. Rev. E 63, 046101 (2001). [Journal]
[cited in page: 37]
K. P. O'Keeffe and S. H. Strogatz,
Dynamics of a population of oscillatory and excitable elements,
Phys. Rev. E 93, 062203 (2016). [Journal] [arXiv]
[cited in page: 285]
K. Okuda and Y. Kuramoto,
Mutual entrainment between populations of coupled oscillators,
Prog. Theor. Phys. 86, 1159 (1991). [Journal]
[cited in page: 317]
K. Okuda,
Variety and generality of clustering in globally coupled oscillators,
Physica D 63, 424 (1993). [Journal]
[cited in page: 217]
R. Olfati-Saber, J. A. Fax, and R. M. Murray,
Consensus and cooperation in networked multi-agent systems,
Proc. IEEE 95, 215 (2007). [Journal]
[cited in page: 32]
O. E. Omel'chenko and M. Wolfrum,
Nonuniversal transitions to synchrony in the Sakaguchi-Kuramoto model,
Phys. Rev. Lett. 109, 164101 (2012). [Journal]
[cited in page: 279]
O. E. Omel'chenko and M. Wolfrum,
Bifurcations in the Sakaguchi-Kuramoto model,
Physica D 263, 74 (2013). [Journal]
[cited in page: 279]
O. E. Omel'chenko, M. Wolfrum, and C. R. Laing,
Partially coherent twisted states in arrays of coupled phase oscillators,
Chaos 24, 023102 (2014). [Journal]
[cited in page: 297]
O. E. Omel'chenko and M. Wolfrum,
Is there an impact of small phase lags in the Kuramoto model?,
Chaos 26, 094806 (2016). [Journal]
[cited in page: 279]
P. Ortoleva and J. Ross,
Phase waves in oscillatory chemical reactions,
J. Chem. Phys. 58, 5673 (1973). [Journal]
[cited in page: 165]
K. Ota, M. Nomura, and T. Aoyagi,
Weighted spike-triggered average of a fluctuating stimulus yielding the phase response curve,
Phys. Rev. Lett. 103, 024101 (2009). [Journal] [arXiv]
[cited in page: 150]
K. Ota, T. Omori, S. Watanabe, H. Miyakawa, M. Okada, and T. Aonishi,
Measurement of infinitesimal phase response curves from noisy real neurons,
Phys. Rev. E 84, 041902 (2011). [Journal]
[cited in page: 150]
E. Ott,
Chaos in Dynamical Systems
(Cambridge University Press, Second Edition, Cambridge, 2002). [Amazon]
[cited in page: 115]
E. Ott and T. M. Antonsen,
Low dimensional behavior of large systems of globally coupled oscillators,
Chaos 18, 037113 (2008). [Journal] [arXiv]
[cited in pages: 276, 277]
E. Ott, J. H. Platig, T. M. Antonsen, and M. Girvan,
Echo phenomena in large systems of coupled oscillators,
Chaos 18, 037115 (2008). [Journal] [arXiv]
[cited in page: 254]
E. Ott and T. M. Antonsen,
Long time evolution of phase oscillator systems,
Chaos 19, 023117 (2009). [Journal] [arXiv]
[cited in page: 279]
E. Ott, B. R. Hunt, and T. M. Antonsen,
Comment on ``Long time evolution of phase oscillator systems'' [Chaos 19, 023117 (2009)],
Chaos 21, 025112 (2011). [Journal] [arXiv]
[cited in page: 279]
Q. Ouyang and H. Swinney,
Transition from a uniform state to hexagonal and striped Turing patterns,
Nature 352, 610 (1991). [Journal]
[cited in page: 22]
K. Pakdaman,
The reliability of the stochastic active rotator,
Neural Comput. 14, 781 (2002). [Journal]
[cited in page: 192]
M. J. Panaggio and D. M. Abrams,
Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators,
Nonlinearity 28, R67 (2015). [Journal] [arXiv]
[cited in page: 272]
J. Pantaleone,
Synchronization of metronomes,
Am. J. Phys. 70, 992 (2002). [Journal]
[cited in page: 6]
Y. Park and G. B. Ermentrout,
Weakly coupled oscillators in a slowly varying world,
J. Comput. Neurosci. 40, 269 (2016). [Journal] [arXiv]
[cited in page: 204]
D. Pazo and E. Montbrio,
Existence of hysteresis in the Kuramoto model with bimodal frequency distributions,
Phys. Rev. E 80, 046215 (2009). [Journal] [arXiv]
[cited in page: 282]
D. Pazo and E. Montbrio,
Low-dimensional dynamics of populations of pulse-coupled oscillators,
Phys. Rev. X 4, 011009 (2014). [Journal] [arXiv]
[cited in page: 285]
C. S. Peskin,
Mathematical Aspects of Heart Physiology
(Courant Institute of Mathematical Sciences, 1975). [Author]
[cited in page: 24]
A. Pikovsky and S. Ruffo,
Finite-size effects in a population of interacting oscillators,
Phys. Rev. E 59, 1633 (1999). [Journal]
[cited in page: 294]
A. Pikovsky, M. Rosenblum, and J. Kurths,
Synchronization: A Universal Concept in Nonlinear Sciences
(Cambridge University Press, Cambridge, 2001). [Amazon]
[徳田功 訳: 同期理論の基礎と応用 (丸善, 2009).] [Amazon]
[cited in pages: 3, 5]
A. Pikovsky and M. Rosenblum,
Partially integrable dynamics of hierarchical populations of coupled oscillators,
Phys. Rev. Lett. 101, 264103 (2008). [Journal] [arXiv]
[cited in pages: 214, 234, 283]
A. Pikovsky and M. Rosenblum,
Dynamics of heterogeneous oscillator ensembles in terms of collective variables,
Physica D 240, 872 (2011). [Journal]
[cited in page: 285]
A. Pikovsky and M. Rosenblum,
Dynamics of globally coupled oscillators: progress and perspectives,
Chaos 25, 097616 (2015). [Journal] [arXiv]
[cited in page: 232]
A. Pikovsky,
Maximizing coherence of oscillations by external locking,
Phys. Rev. Lett. 115, 070602 (2015). [Journal] [arXiv]
[cited in page: 155]
O. V. Popovych, C. Hauptmann, and P. A. Tass,
Effective desynchronization by nonlinear delayed feedback,
Phys. Rev. Lett. 94, 164102 (2005). [Journal]
[cited in page: 10]
O. V. Popovych, C. Hauptmann, and P. A. Tass,
Desynchronization and decoupling of interacting oscillators by nonlinear delayed feedback,
Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, 1977 (2006). [Journal]
[cited in page: 10]
S. Popp, O. Stiller, I. S. Aranson, A. Weber, and L. Kramer,
Localized hole solutions and spatiotemporal chaos in the 1D complex Ginzburg-Landau equation,
Phys. Rev. Lett. 70, 3880 (1993). [Journal]
[cited in page: 108]
S. Popp, O. Stiller, I. S. Aranson, and L. Kramer,
Hole solutions in the 1D complex Ginzburg-Landau equation,
Physica D 84, 398 (1995). [Journal] [arXiv]
[cited in page: 108]
I. Prigogine and R. Lefever,
Symmetry breaking instabilities in dissipative systems. II,
J. Chem. Phys. 48, 1695 (1968). [Journal]
[cited in page: 23]
D. D. Quinn, R. H. Rand, and S. H. Strogatz,
Singular unlocking transition in the Winfree model of coupled oscillators,
Phys. Rev. E 75, 036218 (2007). [Journal]
[cited in page: 231]
S. M. Reppert and D. R. Weaver,
Coordination of circadian timing in mammals,
Nature 418, 935 (2002). [Journal]
[cited in page: 9]
J. G. Restrepo, E. Ott, and B. R. Hunt,
Onset of synchronization in large networks of coupled oscillators,
Phys. Rev. E 71, 036151 (2005). [Journal] [arXiv]
[cited in page: 258]
J. G. Restrepo, E. Ott, and B. R. Hunt,
Synchronization in large directed networks of coupled phase oscillators,
Chaos 16, 015107 (2006). [Journal] [arXiv]
[cited in page: 258]
H. Risken,
The Fokker-Planck Equation:
Methods of Solutions and Applications
(Springer, Berlin, 1989). [Amazon]
[cited in page: 181]
J. Rit,
Evaluation of entrainment of a nonlinear neural oscillator to white noise,
Phys. Rev. E 68, 041915 (2003). [Journal]
[cited in page: 192]
F. A. Rodrigues, T. K. DM. Peron, P. Ji, and J. Kurths,
The Kuramoto model in complex networks,
Phys. Rep. 610, 1 (2016). [Journal] [arXiv]
[cited in page: 232]
M. Rosenblum and A. Pikovsky,
Controlling synchronization in an ensemble of globally coupled oscillators,
Phys. Rev. Lett. 92, 114102 (2004). [Journal]
[cited in page: 10]
M. Rosenblum and A. Pikovsky,
Delayed feedback control of collective synchrony:
An approach to suppression of pathological brain rhythms,
Phys. Rev. E 70, 041904 (2004). [Journal]
[cited in page: 10]
O. Rudzick and A. S. Mikhailov,
Front reversals, wave traps, and twisted spirals in periodically forced oscillatory media,
Phys. Rev. Lett. 96, 018302 (2006). [Journal]
[cited in page: 122]
T. Saigusa, A. Tero, T. Nakagaki, and Y. Kuramoto,
Amoebae anticipate periodic events,
Phys. Rev. Lett. 100, 018101 (2008). [Journal] [Amazon]
[cited in page: 254]
H. Sakaguchi and Y. Kuramoto,
A soluble active rotator model showing phase transitions via mutual entrainment,
Prog. Theor. Phys. 76, 576 (1986). [Journal]
[cited in page: 244]
H. Sakaguchi, S. Shinomoto, and Y. Kuramoto,
Local and global self-entrainments in oscillator lattices,
Prog. Theor. Phys. 77, 1005 (1987). [Journal] [CiNii]
[cited in page: 258]
H. Sakaguchi,
Cooperative phenomena in coupled oscillator systems under external fields,
Prog. Theor. Phys. 79, 39 (1988). [Journal]
[cited in pages: 235, 248, 284]
H. Sakaguchi, S. Shinomoto, and Y. Kuramoto,
Mutual entrainment in oscillator lattices with nonvariational type interaction,
Prog. Theor. Phys. 79, 1069 (1988). [Journal] [CiNii]
[cited in page: 161]
H. Sakaguchi,
Instability of the hole solution in the complex Ginzburg-Landau equation,
Prog. Theor. Phys. 85, 417 (1991). [Journal]
[cited in page: 107]
S. Sasa and T. Iwamoto,
Stability of phase-singular solutions to the one-dimensional complex Ginzburg-Landau equation,
Phys. Lett. A 175, 289 (1993). [Journal]
[cited in page: 108]
K. Sato, Y. Kuramoto, M. Ohtaki, Y. Shimamoto, and S. Ishiwata,
Locally and globally coupled oscillators in muscle,
Phys. Rev. Lett. 111, 108104 (2013). [Journal]
[cited in page: 272]
K. Sato and S. I. Shima,
Various oscillation patterns in phase models with locally attractive and globally repulsive couplings,
Phys. Rev. E 92, 042922 (2015). [Journal]
[cited in page: 273]
G. S. Schmidt, D. Wilson, F. Allgower, and J. Moehlis,
Selective averaging with application to phase reduction and neural control,
Nonlinear Theory and Its Applications IEICE 5, 424 (2014). [Journal]
[cited in page: 178]
L. A. Segel,
The non-linear interaction of two disturbances in the thermal convection problem,
J. Fluid Mech. 14, 97 (1962). [Journal]
[cited in page: 64]
G. C. Sethia, A. Sen, and F. M. Atay,
Clustered chimera states in delay-coupled oscillator systems,
Phys. Rev. Lett. 100, 144102 (2008). [Journal] [arXiv]
[cited in page: 265]
X. Shao, Y. Wu, J. Zhang, H. Wang, and Q. Ouyang,
Inward propagating chemical waves in a single-phase reaction-diffusion system,
Phys. Rev. Lett. 100, 198304 (2008). [Journal]
[cited in pages: 22, 30]
J. H. Sheeba, V. K. Chandrasekar, A. Stefanovska, and P. V. E. McClintock,
Routes to synchrony between asymmetrically interacting oscillator ensembles,
Phys. Rev. E 78, 025201(R) (2008). [Journal] [arXiv]
[cited in page: 317]
J. H. Sheeba, V. K. Chandrasekar, A. Stefanovska, and P. V. E. McClintock,
Asymmetry-induced effects in coupled phase-oscillator ensembles: Routes to synchronization,
Phys. Rev. E 79, 046210 (2009). [Journal] [arXiv]
[cited in page: 317]
S. I. Shima and Y. Kuramoto,
Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators,
Phys. Rev. E 69, 036213 (2004). [Journal] [arXiv]
[cited in pages: 265, 266, 267, 270]
S. Shinomoto and Y. Kuramoto,
Phase transitions in active rotator systems,
Prog. Theor. Phys. 75, 1105 (1986). [Journal]
[cited in page: 285]
Y. Shiogai and Y. Kuramoto,
Wave propagation in nonlocally coupled oscillators with noise,
Prog. Theor. Phys. Suppl. 150, 435 (2003). [Journal] [arXiv]
[cited in page: 288]
B. I. Shraiman, A. Pumir, W. van Saarloos, P. C. Hohenberg, H. Chate, and M. Holen,
Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation,
Physica D 57, 241 (1992). [Journal]
[cited in page: 115]
G. I. Sivashinsky,
Nonlinear analysis of hydrodynamic instability in laminar flames.
I. Derivation of basic equations,
Acta Astronautica 4, 1177 (1977). [Journal]
[cited in page: 89]
P. S. Skardal, E. Ott, and J.G. Restrepo,
Cluster synchrony in systems of coupled phase oscillators with higher-order coupling,
Phys. Rev. E 84, 036208 (2011). [Journal] [arXiv]
[cited in page: 285]
H. M. Smith,
Synchronous flashing of fireflies,
Science 82, 151 (1935). [Journal]
[cited in page: 9]
P. So, T. B. Luke, and E. Barreto,
Networks of theta neurons with time-varying excitability:
Macroscopic chaos, multistability, and final-state uncertainty,
Physica D 267, 16 (2014). [Journal]
[cited in page: 285]
K. Stewartson and J. T. Stuart,
A non-linear instability theory for a wave system in plane Poiseuille flow,
J. Fluid Mech. 48, 529 (1971). [Journal]
[cited in page: 64]
S. H. Strogatz and R. E. Mirollo,
Stability of incoherence in a population of coupled oscillators,
J. Stat. Phys. 63, 613 (1991). [Journal]
[cited in pages: 246, 257]
S. H. Strogatz, R. E. Mirollo, and P. C. Matthews,
Coupled nonlinear oscillators below the synchronization threshold:
Relaxation by generalized Landau damping,
Phys. Rev. Lett. 68, 2730 (1992). [Journal]
[cited in pages: 252(2), 253]
S. H. Strogatz and R. E. Mirollo,
Splay states in globally coupled Josephson arrays:
Analytical prediction of Floquet multipliers,
Phys. Rev. E 47, 220 (1993). [Journal]
[cited in page: 26]
S. H. Strogatz,
From Kuramoto to Crawford:
exploring the onset of synchronization in populations of coupled oscillators,
Physica D 143, 1 (2000). [Journal]
[cited in page: 232]
S. H. Strogatz,
Nonlinear Dynamics and Chaos:
With Applications to Physics, Biology, Chemistry, and Engineering
(Westview Press, MA, 2001). [Amazon]
[田中久陽・中尾裕也・千葉逸人 訳: 非線形ダイナミクスとカオス (丸善,2015).] [Amazon]
[cited in pages: 3, 36]
S. H. Strogatz,
Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life
(Hyperion Books, New York, 2003). [Amazon] [TED]
[蔵本由紀 監修/長尾力 訳: SYNC (早川書房, 2005).] [Amazon]
[cited in pages: 3, 10]
S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott,
Theoretical mechanics: Crowd synchrony on the Millennium Bridge,
Nature 438, 43 (2005). [Journal] [YouTube]
[cited in pages: 10, 206, 245]
J. T. Stuart,
On the non-linear mechanics of wave disturbances in stable and unstable parallel flows,
Part 1. The basic behaviour in plane Poiseuille flow,
J. Fluid Mech. 9, 353 (1960). [Journal]
[cited in page: 60]
J. T. Stuart and R. C. DiPrima,
On the mathematics of Taylor-vortex flows in cylinders of finite length,
Proc. R. Soc. London A 372, 357 (1980). [Journal]
[cited in page: 77]
Y. Suda and K. Okuda,
Persistent chimera states in nonlocally coupled phase oscillators,
Phys. Rev. E 92, 060901(R) (2015). [Journal]
[cited in page: 265]
S. Sunada, K. Arai, K. Yoshimura, and M. Adachi,
Optical phase synchronization by injection of common broadband low-coherent light,
Phys. Rev. Lett. 112, 204101 (2014). [Journal]
[cited in page: 195]
K. A. Takeuchi, F. Ginelli, and H. Chate,
Lyapunov analysis captures the collective dynamics of large chaotic systems,
Phys. Rev. Lett. 103, 154103 (2009). [Journal] [arXiv]
[cited in page: 229]
D. Tanaka and Y. Kuramoto,
Complex Ginzburg-Landau equation with nonlocal coupling,
Phys. Rev. E 68, 026219 (2003). [Journal] [arXiv]
[cited in page: 69]
D. Tanaka,
Chemical turbulence equivalent to Nikolaevskii turbulence,
Phys. Rev. E 70, 015202 (2004). [Journal] [arXiv]
[cited in page: 89]
D. Tanaka,
General chemotactic model of oscillators,
Phys. Rev. Lett. 99, 134103 (2007). [Journal] [arXiv]
[cited in page: 69]
田中久陽,
同期現象の科学の最近の進展,
電子情報通信学会誌 80, 1175 (1997). [CiNii]
[cited in page: 32]
田中久陽・大石進一,
同期技術と同期現象,
日本物理学会誌 53, 200 (1998). [CiNii]
[cited in page: 32]
H. Tanaka, H. Nakao, and K. Shinohara,
Self-organizing timing allocation mechanism in distributed wireless sensor networks,
IEICE Electron. Express 6, 1562 (2009). [Journal]
[cited in pages: 32, 209]
H. Tanaka,
Synchronization limit of weakly forced nonlinear oscillators,
J. Phys. A: Math. Theor. 47, 402002 (2014). [Journal]
[cited in page: 155]
H. Tanaka,
Optimal entrainment with smooth, pulse, and square signals in weakly forced nonlinear oscillators,
Physica D 288, 1 (2014). [Journal]
[cited in page: 155]
H. Tanaka, I. Nishikawa, J. Kurths, Y. Chen, and I. Z. Kiss,
Optimal synchronization of oscillatory chemical reactions with complex pulse, square, and smooth waveforms signals maximizes Tsallis entropy,
Eur. Phys. Lett. 111, 50007 (2015). [Journal] [IEICE]
[cited in page: 155]
T. Taniuti and C.-C. Wei,
Reductive perturbation method in nonlinear wave propagation. I,
J. Phys. Soc. Jpn. 24, 941 (1968). [Journal]
[cited in page: 36]
T. Taniuti,
Reductive perturbation method and far fields of wave equations,
Prog. Theor. Phys. Suppl. 55, 1 (1974). [Journal]
[cited in page: 36]
P. A. Tass,
Phase Resetting in Medicine and Biology: Stochastic Modelling and Data Analysis
(Springer, New York, 1999). [Amazon]
[cited in page: 10]
T. Tateno and H. P. C. Robinson,
Phase resetting curves and oscillatory stability in interneurons of rat somatosensory cortex,
Biophys. J. 92, 683 (2007). [Journal]
[cited in page: 145]
A. F. Taylor, M. R. Tinsley, F. Wang, Z. Huang, and K. Showalter,
Dynamical quorum sensing and synchronization in large populations of chemical oscillators,
Science 323, 614 (2009). [Journal]
[cited in page: 12]
J. N. Teramae and D. Tanaka,
Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators,
Phys. Rev. Lett. 93, 204103 (2004). [Journal] [arXiv]
[cited in page: 192]
J. N. Teramae and D. Tanaka,
Noise induced phase synchronization of a general class of limit cycle oscillators,
Prog. Theor. Phys. Suppl. 161, 360 (2006). [Journal]
[cited in page: 196]
J. N. Teramae and T. Fukai,
Temporal precision of spike response to fluctuating input in pulse-coupled networks of oscillating neurons,
Phys. Rev. Lett. 101, 248105 (2008). [Journal] [arXiv]
[cited in page: 196]
J. N. Teramae, H. Nakao, and G. B. Ermentrout,
Stochastic phase reduction for a general class of noisy limit cycle oscillators,
Phys. Rev. Lett. 102, 194102 (2009). [Journal] [arXiv]
[cited in page: 192]
M. Timme and J. Casadiego,
Revealing networks from dynamics: an introduction,
J. Phys. A: Math. Theor. 47, 343001 (2014). [Journal] [arXiv]
[cited in page: 168]
M. R. Tinsley, S. Nkomo, and K. Showalter,
Chimera and phase-cluster states in populations of coupled chemical oscillators,
Nature Physics 8, 662 (2012). [Journal]
[cited in page: 272]
R. Toenjes and B. Blasius,
Perturbation analysis of complete synchronization in networks of phase oscillators,
Phys. Rev. E 80, 026202 (2009). [Journal] [arXiv]
[cited in page: 316]
R. Toenjes,
Synchronization transition in the Kuramoto model with colored noise,
Phys. Rev. E 81, 055201(R) (2010). [Journal] [arXiv]
[cited in page: 286]
I. T. Tokuda, S. Jain, I. Z. Kiss, and J. L. Hudson,
Inferring phase equations from multivariate time series,
Phys. Rev. Lett. 99, 064101 (2007). [Journal]
[cited in page: 168]
R. Toth, A. F. Taylor, and M. R. Tinsley,
Collective behavior of a population of chemically coupled oscillators,
J. Phys. Chem. B 110, 10170 (2006). [Journal]
[cited in pages: 12, 21]
M. I. Tribelsky and K. Tsuboi,
New scenario for transition to turbulence?,
Phys. Rev. Lett. 76, 1631 (1996). [Journal]
[cited in page: 89]
M. I. Tribelsky and M. G. Velarde,
Short-wavelength instability in systems with slow long-wavelength dynamics,
Phys. Rev. E 54, 4973 (1996). [Journal]
[cited in page: 89]
K. Y. Tsang, R. E. Mirollo, S. H. Strogatz, and K. Wiesenfeld,
Dynamics of a globally coupled oscillator array,
Physica D 48, 102 (1991). [Journal]
[cited in pages: 26, 213]
Y. Tsubo, M. Takada, A. D. Reyes, and T. Fukai,
Layer and frequency dependencies of phase response properties of pyramidal neurons in rat motor cortex,
Eur. J. Neurosci. 25, 3429 (2007). [Journal]
[cited in page: 145]
J. J. Tyson and P. C. Fife,
Target patterns in a realistic model of the Belousov-Zhabotinsky reaction,
J. Chem. Phys. 73, 2224 (1980). [Journal]
[cited in page: 19]
A. Uchida, R. McAllister, and R. Roy,
Consistency of nonlinear system response to complex drive signals,
Phys. Rev. Lett. 93, 244102 (2004). [Journal]
[cited in page: 196(2)]
P. J. Uhlhaas and W. Singer,
Neural synchrony in brain disorders:
relevance for cognitive dysfunctions and pathophysiology,
Neuron 52, 155 (2006). [Journal]
[cited in page: 9]
H. Ukai, T. J. Kobayashi, M. Nagano, K. Masumoto, M. Sujino, T. Kondo, K. Yagita, Y. Shigeyoshi, and H. R. Ueda,
Melanopsin-dependent photo-perturbation reveals desynchronization underlying the singularity of mammalian circadian clocks,
Nat. Cell Biol. 9, 1327 (2007). [Journal]
[cited in pages: 13, 145]
N. G. van Kampen,
Stochastic Processes in Physics and Chemistry
(North-Holland, Amsterdam, 1992). [Amazon]
[cited in page: 181]
C. van Vreeswijk, L. F. Abbott, and G. B. Ermentrout,
When inhibition not excitation synchronizes neural firing,
J. Comput. Neurosci. 1, 313 (1994). [Journal]
[cited in page: 161]
V. K. Vanag and I. R. Epstein,
Inwardly rotating spiral waves in a reaction-diffusion system,
Science 294, 835 (2001). [Journal]
[cited in page: 21(2)]
V. K. Vanag and I. R. Epstein,
Packet waves in a reaction-diffusion system,
Phys. Rev. Lett. 88, 088303 (2002). [Journal]
[cited in page: 21]
C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio,
Self-synchronization and dissipation-induced threshold in collective atomic recoil lasing,
Phys. Rev. Lett. 93, 083601 (2004). [Journal] [arXiv]
[cited in page: 12]
T. J. Walker,
Acoustic synchrony: Two mechanisms in the snowy tree cricket,
Science 166, 891 (1969). [Journal]
[cited in page: 6]
S. Watanabe and S. H. Strogatz,
Integrability of a globally coupled oscillator array,
Phys. Rev. Lett. 70, 2391 (1993). [Journal]
[cited in page: 211]
S. Watanabe and S. H. Strogatz,
Constants of motion for superconducting Josephson arrays,
Physica D 74, 197 (1994). [Journal]
[cited in page: 211]
M. Wickramasinghe and I. Z. Kiss,
Spatially organized dynamical states in chemical oscillator networks:
Synchronization, dynamical differentiation, and chimera patterns,
PLoS ONE 8, e80586 (2013). [Journal]
[cited in page: 272]
M. Wickramasinghe and I. Z. Kiss,
Spatially organized partial synchronization through the chimera mechanism in a network of electrochemical reactions,
Phys. Chem. Chem. Phys. 16, 18360 (2014). [Journal]
[cited in page: 272]
K. Wiesenfeld and J. W. Swift,
Averaged equations for Josephson junction series arrays,
Phys. Rev. E 51, 1020 (1995). [Journal]
[cited in pages: 26, 174]
K. Wiesenfeld, P. Colet, and S. H. Strogatz,
Synchronization transitions in a disordered Josephson series array,
Phys. Rev. Lett. 76, 404 (1996). [Journal]
[cited in pages: 174, 245]
K. Wiesenfeld, P. Colet, and S. H. Strogatz,
Frequency locking in Josephson arrays: Connection with the Kuramoto model,
Phys. Rev. E 57, 1563 (1998). [Journal]
[cited in page: 174]
A. T. Winfree,
Biological rhythms and the behavior of populations of coupled oscillators,
J. Theor. Biol. 16, 15 (1967). [Journal]
[cited in page: 230]
A. T. Winfree,
Integrated view of resetting a circadian clock,
J. Theor. Biol. 28, 327 (1970). [Journal]
[cited in page: 149]
A. T. Winfree,
Patterns of phase compromise in biological cycles,
J. Math. Biol. 1, 73 (1974) [Journal]
[cited in pages: 130, 132]
A. T. Winfree,
The Geometry of Biological Time
(Springer, New York, 1980; Springer, Second Edition, New York, 2001). [Amazon]
[cited in pages: 4, 10]
M. Wolfrum, O. E. Omel'chenko, S. Yanchuk, and Y. L. Maistrenko,
Spectral properties of chimera states,
Chaos 21, 013112 (2011). [Journal]
[cited in page: 265]
M. Wolfrum, S. V. Gurevich, and O. E. Omel'chenko,
Turbulence in the Ott-Antonsen equation for arrays of coupled phase oscillator,
Nonlinearity 29, 257 (2016). [Journal]
[cited in pages: 297, 309]
T. Yamada and Y. Kuramoto,
Spiral waves in a nonlinear dissipative system,
Prog. Theor. Phys. 55, 2035 (1976). [Journal]
[cited in page: 89]
T. Yamada and Y. Kuramoto,
A reduced model showing chemical turbulence,
Prog. Theor. Phys. 56, 681 (1976). [Journal]
[cited in page: 103]
K. Yoshida, K. Sato, and A. Sugamata,
Noise-induced synchronization of uncoupled nonlinear systems,
J. Sound Vib. 290, 34 (2006). [Journal]
[cited in page: 196]
K. Yoshimura and K. Arai,
Phase reduction of stochastic limit cycle oscillators,
Phys. Rev. Lett. 101, 154101 (2008). [Journal] [arXiv]
[cited in page: 191]
K. Yoshimura, P. Davis, and A. Uchida,
Invariance of frequency difference in nonresonant entrainment of detuned oscillators induced by common white noise,
Prog. Theor. Phys. 120, 621 (2008). [Journal]
[cited in page: 196]
Y. Zhai, I. Z. Kiss, and J. L. Hudson,
Emerging coherence of oscillating chemical reactions on arrays:
experiments and simulations,
Ind. Eng. Chem. Res. 43, 315 (2004). [Journal]
[cited in page: 245]
T. Zhou, L. Chen, and K. Aihara,
Molecular communication through stochastic synchronization induced by extracellular fluctuations,
Phys. Rev. Lett. 95, 178103 (2005). [Journal]
[cited in page: 196]
A. Zlotnik, Y. Chen, I. Z. Kiss, H. Tanaka, and J.-S. Li,
Optimal waveform for fast entrainment of weakly forced nonlinear oscillators,
Phys. Rev. Lett. 111, 024102 (2013). [Journal]
[cited in page: 155]
A. Zlotnik, R. Nagao, I. Z. Kiss, and J.-S. Li,
Phase-selective entrainment of nonlinear oscillator ensembles,
Nature Communications 7, 10788 (2016). [Journal]
[cited in page: 155]