Publications

Journal articles

• M. Fadera, C. M. Postlethwaite and P. Ashwin, Network Attractors and Nonlinear Dynamics of Neural Computation, to appear in Current Opinion in Neurobiology, 2023.

• D. Groothuizen Dijkema and C. M. Postlethwaite, Travelling waves and heteroclinic networks in models of spatially-extended cyclic competition, Nonlinearity, 36, 6546, 2023. 

• V. Jeong and C. Postlethwaite, Effect of noise on residence times of a heteroclinic cycle, Dynamical Systems, an International Journal, 2022.

• C.M. Postlethwaite and R. Sturman, Stability of heteroclinic cycles in ring graphs, Chaos, 32, 063104, 2022.

• C.M. Postlethwaite and A.M. Rucklidge, Stability of cycling behaviour near a heteroclinic network model of Rock-Paper-Scissors-Lizard-Spock. Nonlinearity, 35, 1702, 2022.

• P. Ashwin and C. Postlethwaite, Excitable networks for finite state computation with continuous time recurrent neural networks. Biological Cybernetics, 115(4), 2021.

• C. Hasan, H. Osinga, C. Postlethwaite and A. Rucklidge, Numerical continuation of spiral waves in heteroclinic networks of cyclic dominance.  IMA Journal of Applied Mathematics, 86, 1141-1163, 2021.

• C. Hasan, H. Osinga, C. Postlethwaite and A. Rucklidge, Spatiotemporal stability of periodic travelling waves in a heteroclinic-cycle model, Nonlinearity, 34, 5576-5598, 2021.

• J. Creaser, P. Ashwin, C. Postlethwaite, and J. Britz. Noisy network attractor models for transitions between EEG microstates. J. Math. Neurosc. 11, 1, 2021. 

• A. Ceni, P. Ashwin, L. Livi and C. Postlethwaite, The echo index and multistability in input-driven recurrent neural networks, Physica D: Nonlinear Phenomena, 412, 2020.

• P. Gandhi, M. Golubitsky, C. M. Postlethwaite, I. Stewart and Y. Wang.  Bifurcations on Fully Inhomogenous Networks. SIAM J. Appl. Dyn. Syst., 19(1), 366–411, 2020.

• M.D. Egbert, V. Jeong and C.M. Postlethwaite, Where computation and dynamics meet: heteroclinic network-based controllers in evolutionary robotic. IEEE Transactions on Neural Networks and Learning Systems, 2019.

• M. Egbert, A. Keane, C. Postlethwaite and N. Wong, Can signal delay be functional? Including delay in evolved robot controllers. Artificial Life, 25:4, 2019, 315-333.

• C.M. Postlethwaite and A.M. Rucklidge, A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock-Paper-Scissors. Nonlinearity, 32(4), 2019, 1375-1407. 


• P. Ashwin and C.M. Postlethwaite, Sensitive Finite-State Computations Using a Distributed Network with a Noisy Network Attractor, IEEE Transactions on Neural Networks and Learning Systems, 99, 2018, 1-12.

• A. Keane, B. Krauskopf and C.M. Postlethwaite, Climate models with delay differential equations, Chaos, 27(11), 2017, 114309.

• C.M. Postlethwaite and A.M. Rucklidge, Spirals and heteroclinic cycles in a spatially extended Rock-Paper-Scissors model of cyclic dominance. EPL. 117(4) 2017, 48006.

• P. Ashwin and C.M. Postlethwaite, Quantifying noisy attractors: From heteroclinic to excitable networks. SIAM Journal on Applied Dynamical Systems. 15(5) 2016, 1989-2016.

• A. Keane, B. Krauskopf and C.M. Postlethwaite, Investigating irregular behavior in a model for the El Nino Southern Oscillation with positive and negative delayed feedback. SIAM Journal on Applied Dynamical Systems. 15(3) 2016, 1656-1689.

• R.M. Turner, M.M. Walker and C.M. Postlethwaite, Literal grid map models for animal navigation: Assumptions and predictions. Journal of Theoretical Biology. 404 2016, 169-181.

• P. Ashwin and C.M. Postlethwaite, Designing heteroclinic and excitable networks in phase space using two populations of coupled cells. Journal of Nonlinear Science. 26(2) 2016, 345-364.

• A. Keane, B. Krauskopf and C.M. Postlethwaite, Delayed feedback versus seasonal forcing: resonance phenomena in an El Niño Southern Oscillation model. SIAM Journal on Applied Dynamical Systems 14(3) 2015, 1229-1257.

• A.S. Purewal, C.M. Postlethwaite and B. Krauskopf, A global bifurcation analysis of the subcritical Hopf normal form subject to Pyragas time-delayed feedback control. SIAM Journal on Applied Dynamical Systems 13(4) 2014, 1879-1915. 

• A.S. Purewal, C.M. Postlethwaite and B. Krauskopf, Effect of delay mismatch in Pyragas feedback control. Physical Review E, 90, 2014, 052905.

• C. M. Postlethwaite and M. Walker, A model for navigational errors in complex environmental fields. Journal of Theoretical Biology, 363, 2014, 134-144.

• P. Ashwin and C.M. Postlethwaite, On designing heteroclinic networks from graphs. Physica D, 265, 2013, 26-39. 

• Claire M. Postlethwaite and Todd Dennis, Effects of temporal resolution on an inferential model of animal movement. PLoS One, 8(5), 2013 e57640.

• Claire M. Postlethwaite, G.Brown and M.Silber, Feedback control of unstable periodic orbits in equivariant Hopf bifurcations. Philosophical Transactions of the Royal Society A. 371, 2013.

• C.M.Postlethwaite, P.Brown and T.E.Dennis, A new multi-scale measure for analysing animal tracking data. Journal of Theoretical Biology, 317, 2013, 175-185.

• Vivien Kirk, Claire M. Postlethwaite and Alastair M. Rucklidge, Resonance in heteroclinic networks. SIADS 11(4), 2012, 1360-1401.

• M. Golubitsky and C. M. Postlethwaite, Feed-forward networks, center manifolds, and forcing. Discrete and Continuous Dynamical Systems, Series A, 32(8), 2012, 2913-2935.

• G. Brown, C. M. Postlethwaite and M. Silber, Time-delayed feedback control of unstable periodic orbits near a subcritical Hopf bifurcation. Physica D, 240, 2011, 859-871.

• C. M. Postlethwaite and M. Walker, A geometric model for initial orientation errors in pigeon navigation. Journal of Theoretical Biology, 269, 2011, 273-279. 

• Claire M. Postlethwaite, A new mechanism for stability loss from a heteroclinic cycle. Dynamical Systems: An International Journal, 25(3), 2010, 305-322. 

• V. Kirk, E. Lane, C. M. Postlethwaite, A. M. Rucklidge, and M. Silber, A mechanism for switching near a heteroclinic network. Dynamical Systems: An International Journal, 25(3), 2010, 323-349. 

• Claire M. Postlethwaite and J.H.P. Dawes, Resonance bifurcations from robust homoclinic cycles. Nonlinearity 23, 2010, 621-642. 

• Claire M. Postlethwaite, Tiffany M. Psemeneki, Jangir Selimkhanov, Mary Silber and Malcolm A. MacIver, Optimal movement in the prey strikes of weakly electric fish: A case study of the interplay of body plan and movement capability. Roy. Soc. Interface, 6(34), 2009, 417-433. 

• C. M. Postlethwaite, Stabilization of long-period periodic orbits using time-delayed feedback control. SIADS, 8, 2009, 21-39. 

• Claire M. Postlethwaite and Mary Silber, Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control. Phys. Rev. E, 76, 2007, 056214. http://arxiv.org

• Claire M. Postlethwaite and Mary Silber, Spatial and temporal feedback of traveling wave solutions of the two-dimensional complex Ginzburg-Landau equation. Physica D, 236, 2007, 65-74.  http://arxiv.org

• C. M. Postlethwaite and J. H. P. Dawes, A codimension-two resonant bifurcation from a heteroclinic cycle with complex eigenvalues. Dynamical Systems: An International Journal, 21(3), 2006, 313-336. PDF (292KB)

• C. M. Postlethwaite and J. H. P. Dawes, Regular and irregular cycling near a heteroclinic network. Nonlinearity, 18, 2005, 1477-1509.

• J. H. P. Dawes, C. M. Postlethwaite and M. R. E. Proctor, Instabilities induced by a weak breaking of a strong spatial resonance. Physica D, 191, 2004, 1-30.

Book chapters

• M. Golubitsky, C. Postlethwaite, L-J. Shiau and Y. Zhang, The feed-forward chain as a filter amplifier motif.
  In: Coherent Behavior in Neuronal Networks. (K. Josic, M. Matias, R. Romo, and J. Rubin, eds.) Springer, 2009, 95-120. 

• A.S. Purewal, B. Krauskopf and C.M. Postlethwaite, Global effects of time-delayed feedback control applied to the Lorenz system. In: Control of Self-Organizing Nonlinear Systems. (E. Schöll, S.H.L. Klapp and P. Hövel, eds.), Springer Series in Synergetics, Springer-Verlag, 2015.

Refereed conferences proceedings

• Y. Kolezhitskiy, M. D. Egbert, Postlethwaite C., Stochastic Analysis of The Viability of a Protocell, accepted for oral presentation at IEEE SSCI 2022 and inclusion in conference proceedings, 2022.

• M. Egbert, A. Keane, and C. Postlethwaite, Lag in Situated, Embodied and Dynamical Adaptive Systems. In: Advances in Artificial Life, Proceedings of the 14th European Conference on Artificial Life, ECAL, 2017.

• J.E. Paterson, M.O.J. Thomas, C.M. Postlethwaite and S. Taylor, The internal disciplinarian: Who is in control? In: S. Brown, S. Larsen, K. Marrongelle, & M. Oehrtman (Eds.), Proceedings of the 14th Annual Conference on Research in Undergraduate Mathematics Education 2, 2011, 354-368. Portland, Oregon.