Selected Publications

E. P. Zemskov, M. A. Tsyganov, G. R. Ivanitsky, and W. Horsthemke: "Solitary Pulses and Periodic Wave Trains in a Bistable Fitzhugh-Nagumo Model with Cross Diffusion and Cross Advection," Phys. Rev. E, 105, 014207 (10 pages) (2022)

E. P. Zemskov, M. A. Tsyganov, K. Kassner, and W. Horsthemke: "Nonlinear Waves in a Quintic FitzHugh-Nagumo Model with Cross Diffusion: Fronts, Pulses and Wave Trains," Chaos, 31, 033141 (13 pages) (2021)

E. P. Zemskov, M. A. Tsyganov, and W. Horsthemke: "Oscillatory Multipulsons: Dissipative Soliton Trains in Bistable Reaction-Diffusion Systems with Cross Diffusion of Attractive-Repulsive Type," Phys. Rev. E, 101, 032208 (10 pages) (2020)

A. Iomin, V. Méndez, and W. Horsthemke: "Comb model: Non-Markovain versus Markovian," Fractal Fract., 3, 54 (13 pages) (2019)

E. P. Zemskov, M. A. Tsyganov, and W. Horsthemke: "Multifront regime of a piecewise-linear FitzHugh-Nagumo model with cross diffusion," Phys. Rev. E, 99, 062214 (9 pages) (2019)

V. Méndez, M. Asssaf, A. Masó-Puigdellosas, D. Campos, and W. Horsthemke: "Demographic stochasticity and extinction in populations with Allee effect," Phys. Rev. E, 99, 022101 (11 pages) (2019) [Editors' Suggestion]

A. Iomin, V. Méndez, and W. Horsthemke: "Fractional Dynamics in Comb-like Structures" (World Scientific, Singapore, 2018)

E. P. Zemskov, M. A. Tsyganov, and W. Horsthemke: "Oscillatory pulse-front waves in a reaction-diffusion system with cross diffusion," Phys. Rev. E, 97, 062206 (8 pages) (2018)

V. Méndez, M. Asssaf, W. Horsthemke, and D. Campos: "Stochastic foundations in nonlinear density-regulation growth," Phys. Rev. E 96, 022147 (11 pages) (2017)

V. Méndez, A. Iomin, W. Horsthemke, and D. Campos: "Langevin dynamics for ramified structures," J. Stat. Mech.: Theor. Exp. 2017, 063205 (18 pages) (2017)

E. P. Zemskov, M. A. Tsyganov, and W. Horsthemke: "Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion," Phys. Rev. E, 95, 012203 (9 pages) (2017)

E. P. Zemskov and W. Horsthemke: "Diffusive instabilities in hyperbolic reaction-diffusion equations," Phys. Rev. E, 93, 032211 (9 pages) (2016)

V. Méndez, A. Iomin, D. Campos, and W. Horsthemke: "Mesoscopic description of random walks on combs," Phys. Rev. E 92, 062112 (9 pages) (2015)

E. P. Zemskov, M. A. Tsyganov, and W. Horsthemke: "Wavy fronts in a hyperbolic FitzHugh-Nagumo system and the effects of cross diffusion," Phys. Rev. E, 91, 062917 (6 pages) (2015)

V. Méndez, M. Asssaf, D. Campos, and W. Horsthemke: "Stochastic dynamics and logistic population growth," Phys. Rev. E 91, 062133 (12 pages) (2015)

V. Méndez, D. Campos, and W. Horsthemke: "Growth and dispersal with inertia: Hyperbolic reaction-transport systems," Phys. Rev. E 90, 042114 (14 pages) (2014)

V. Méndez, S. I. Denisov, D. Campos, and W. Horsthemke: "Role of the interpretation of stochastic calculus in systems with cross-correlated Gaussian white noises," Phys. Rev. E 90, 012116 (11 pages) (2014)

V. Méndez, D. Campos, and W. Horsthemke: "Efficiency of harvesting energy from colored noise by linear oscillators," Phys. Rev. E 88, 022124 (6 pages) (2013)

V. Méndez, D. Campos, and W. Horsthemke: "Stationary energy probability density of oscillators driven by a random external force," Phys. Rev. E 87, 062132 (10 pages) (2013)

E. P. Zemskov, K. Kassner, M. J. B. Hauser, and W. Horsthemke: "Turing space in reaction-diffusion systems with density-dependent cross diffusion," Phys. Rev. E. 87, 032906 (9 pages) (2013)

V. Méndez, D. Campos, and W. Horsthemke: "Stochastic fluctuations of the transmission rate in the susceptible-infected-susceptible epidemic model," Phys. Rev. E 86, 011919 (8 pages) (2012)

V. Méndez, W. Horsthemke, P. Mestres, and D. Campos: "Instabilities of the harmonic oscillator with fluctuating damping," Phys. Rev. E 84, 041137 (8 pages) (2011)

V. Méndez, I. Llopis, D. Campos, and W. Horsthemke: "Effect of environmental fluctuations on invasion fronts," J. Theor. Biol. 281, 31 - 38 (2011)

N. Kumar and W. Horsthemke: "Effects of cross diffusion on Turing bifurcations in two-species reaction-transport systems," Phys. Rev. E 83, 036105 (8 pages) (2011)

V. Méndez, S. Fedotov, and W. Horsthemke: "Reaction-Transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities" (Springer-Verlag, Berlin, 2010)

V. Méndez, I. Llopis, D. Campos, and W. Horsthemke: "Extinction Conditions for Isolated Populations Affected by Environmental Stochasticity," Theor. Popul. Biol. 77, 250 - 256 (2010)

N. Kumar and W. Horsthemke: "Turing Bifurcation in a Reaction-Diffusion System with Density-Dependent Dispersal," Physica A 389, 1812 - 1818 (2010)

V. Méndez, D. Campos, I. Llopis, and W. Horsthemke: "Extinction and Chaotic Patterns in Map Lattices under Hostile Conditions," Bull. Math. Biol. 72, 432 - 443 (2010)

P. K. Moore and W. Horsthemke: "Three-Dimensional Patterns in the Lengyel-Rabai-Epstein Model of the CDIMA Reaction," Chaos 19, 043116 (11 pages) (2009)

S. I. Denisov, W. Horsthemke, and P. Hänggi: "Generalized Fokker-Planck equation: Derivation and exact solutions," Eur. Phys. J. B 68, 567 – 575 (2009)

A. Yadav, S. M. Milu, and W. Horsthemke: "Turing Instability in Reaction-Subdiffusion Systems," Phys. Rev. E 78, 026116 (8 pages) (2008)

S. I. Denisov, W. Horsthemke, and P. Hänggi: "Steady-State Lévy Flights in a Confined Domain," Phys. Rev. E 77, 061112 (4 pages) (2008)

A. Yadav, S. Fedotov, V. Méndez, and W. Horsthemke: "Propagating Fronts in Reaction-Transport Systems with Memory," Phys. Lett. A 371, 374 - 378 (2007)

V. Méndez, W. Horsthemke, E. P. Zemskov, and J Casas-Vázquez: "Segregation and Pursuit Waves in Activator-Inhibitor Systems," Phys. Rev. E 76, 046222 (6 pages) (2007)

V. Méndez, W. Horsthemke, J. Casas-Vázquez, and E. P. Zemskov: "Variational Principles and the Effect of a Cutoff on Population Pattern Size," Eur. Phys. J. ST 146, 189 - 197 (2007)

V. Méndez, S. Fedotov, and W. Horsthemke: "Effect of Memory on the Speed of Reaction-Diffusion Fronts," Europhys. Lett. 77, 58006 (5 pages) (2007)

V. Méndez, S. Fedotov, D. Campos, and W. Horsthemke: "Biased Random Walks and Propagation Failure," Phys. Rev. E 75, 011118 (4 pages) (2007)

A. Yadav and W. Horsthemke: "Kinetic Equations for Reaction-Subdiffusion Systems: Derivation and Stability Analysis," Phys. Rev. E 74, 066118 (10 pages) (2006)

W. Horsthemke, C. E. Zachary, and P. K. Moore: "Instabilities in Networks of Reactors Coupled by Photochemical Feedback," Chem. Phys. Lett. 432, 457 - 461 (2006)

S. I. Denisov, A. N. Vitrenko, W. Horsthemke, and P. Hänggi: "Anomalous Diffusion for Overdamped Particles Driven by Cross-Correlated White Noise Sources," Phys. Rev. E 73, 036120 (6 pages) (2006)

P. K. Moore and W. Horsthemke: "Localized Patterns in Homogeneous Networks of Diffusively Coupled Reactors," Physica D 206, 121 - 144 (2005)

W. Horsthemke: "Pattern Formation in Random Walks with Inertia," in Noise in Complex Systems and Stochastic Dynamics III, edited by L. B. Kish, K. Lindenberg, and Z. Gingl, Proc. of SPIE Vol. 5845 (SPIE, Bellingham, WA, 2005) 12 - 26

W. Horsthemke, K. Lam, and P. K. Moore: "Network Topology and Turing Instabilities in Small Arrays of Diffusively Coupled Reactors," Phys. Lett. A 328, 444 - 451 (2004)

W. Horsthemke and P. K. Moore: "Turing Instability in Inhomogeneous Arrays of Diffusively Coupled Reactors," J. Phys. Chem. A 108, 2225 - 2231 (2004)

S. I. Denisov, A. N. Vitrenko, and W. Horsthemke: "Nonequilibrium Transitions Induced by the Cross-Correlation of White Noise," Phys. Rev. E 68, 046132 (5 pages) (2003)

W. Horsthemke: "External Noise and Front Propagation in Reaction-Transport Systems with Inertia: The Mean Speed of Fisher Waves," Fluct. Noise Lett. 2, R109 - R124 (2002)

S. I. Denisov and W. Horsthemke: "Exactly Solvable Model with an Absorbing State and Multiplicative Colored Gaussian Noise," Phys. Rev. E 65, 061109 (10 pages) (2002)

S. I. Denisov and W. Horsthemke: "Anomalous Diffusion of Particles Driven by Correlated Noise," Phys. Rev. E 62, 7729 - 7734 (2000)

W. Horsthemke: "Fisher Waves in Reaction Random Walks," Phys. Lett. A 263, 285 - 292 (1999)

W. Horsthemke: "Spatial Instabilities in Reaction Random Walks with Direction-Independent Kinetics," Phys. Rev. E 60, 2651 - 2663 (1999)

C. R. Doering, W. Horsthemke, and J. Riordan: "Nonequilibrium Fluctuation-Induced Transport," Phys. Rev. Lett. 72, 2984 - 2987 (1994)

W. Horsthemke, C. R. Doering, T. S. Ray, and M. A. Burschka: "Fluctuations and Correlations in a Diffusion-Reaction System: Unified Description of Internal Fluctuations and External Noise," Phys. Rev. A 45, 5492 - 5503 (1992)

B. Röhricht and W. Horsthemke: "A Bifurcation Sequence to Stationary Spatial Patterns in a Nonuniform Chemical Model System With Equal Diffusion Coefficients," J. Chem. Phys. 94, 4421 - 4426 (1991)

J. E. Pearson and W. Horsthemke: "Turing Instabilities with Nearly Equal Diffusion Coefficients," J. Chem. Phys. 90, 1588 - 1599 (1989)

W. Y. Tam, W. Horsthemke, Z. Noszticzius, and H. L. Swinney: "Sustained Spiral Waves in a Continuously Fed Unstirred Chemical Reactor," J. Chem. Phys. 88, 3395 - 3396 (1988)

Z. Noszticzius, W. Horsthemke, W. D. McCormick, H. L. Swinney, and W. Y. Tam: "Sustained Chemical Waves in an Annular Gel Reactor: A Chemical Pinwheel," Nature 329, 619-620 (1987)

L. Hannon and W. Horsthemke: "Stirring Effects and Bistability in the Iodate-Arsenous Acid Reaction: Premixed Vs Segregated Flows," J. Chem. Phys. 86, 140 - 143 (1987)

W. Horsthemke and R. Lefever: "Noise-Induced Transitions. Theory and Applications in Physics, Chemistry, and Biology" (Springer Verlag, Berlin, 1984; 2nd printing, 2006) (Russian edition: MIR, Moscow, 1987)

W. Horsthemke and R. Lefever: "Voltage-Noise-Induced Transitions in Electrically Excitable Membranes," Biophys. J. 35, 415 - 432 (1981)

R. Lefever and W. Horsthemke: "Multiple Transitions Induced by Light Intensity Fluctuations in Illuminated Chemical Systems," Proc. Natl. Acad. Sci. USA 76, 2490 - 2494 (1979)

L. Arnold, W. Horsthemke, and R. Lefever: "White and Coloured External Noise and Transition Phenomena in Nonlinear Systems," Z. Physik B 29, 367 - 373 (1978)

W. Horsthemke and M. Malek-Mansour: "The Influence of External Noise on Non-Equilibrium Phase Transitions," Z. Physik B 24, 307 - 313 (1976)

W. Horsthemke and A. Bach: "Onsager-Machlup Function for One-Dimensional Nonlinear Diffusion Processes," Z. Physik B 22, 189 - 192 (1975)