Peter Ashwin


Papers to appear , published, preprints, other publications

For later publications, see my current webpage http://emps.exeter.ac.uk/mathematics/staff/pashwin/publications

To Appear

M. Aguiar, P. Ashwin, A. Dias and M. Field. Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation. To appear in Journal of Nonlinear Science (2011) click here for pdf preprint

P. Ashwin and O. Karabacak. Robust Heteroclinic Behaviour, Synchronization, and Ratcheting of Coupled Oscillators. To appear, Randfest (2010)  click here for pdf preprint

T Boonstra, P. Ashwin and M.Breakspear. Multifrequency coordination of cortical oscillations. Abstract for HBM 2011 click here for pdf

Published

2011

O. Podvigina and P. Ashwin. On local attraction properties and a stability index for heteroclinic connections. Nonlinearity 24: 887-929 (2011) Preprint http://arxiv.org/abs/1008.3063

O. Karaback and P. Ashwin. On statistical attractors and the convergence of time averages. Math. Proc.Camb. Phil. Soc.,  150: 353-365 (2011) link to article pdf copy (copyright CUP)

M. Schuster, S. Kilaru, P. Ashwin, C. Lin, N.J. Severs and G. Steinberg. Controlled and stochastic retention concentrates dynein at microtubule ends to keep endosomes on track. doi:10.1038/emboj.2010.360 The EMBO Journal  (2011)

2010

S. Wieczorek, P. Ashwin, C.M. Luke, and P. Cox. Excitability in ramped systems: the compost-bomb instability. Proceedings of The Royal Society A (2010) doi:10.1098/rspa.2010.0485  click here for pdf preprint

P. Ashwin, C. Lin and G. Steinberg. Queueing induced by bidirectional motor motion near the end of a microtubule. Phys. Rev. E 82, 051907 (2010)  http://pre.aps.org/abstract/PRE/v82/i5/e051907 click here for pdf preprint

T. Chawanya and P. Ashwin. A minimal system with a depth-two heteroclinic network. Dynamical Systems 25:397-412 (2010) click here for pdf preprint

P. Ashwin and O. Podvigina. Noise-induced switching near a depth two heteroclinic network, and an application to Boussinesq convection. Chaos http://link.aip.org/link/?CHA/20/023133  (2010) click here for pdf preprint

P. Ashwin, G. Orosz and J. Borresen, Heteroclinic switching in coupled oscillator networks: dynamics on odd graphs.Proceedings of 'Nonlinear Dynamics and Chaos: Advances and Perspectives.' Eds M. Theil, J. Kurths, M.C.  Romano, A. Moura, G. Károlyi, Springer (2010) click here for pdf preprint

A. Azad and P. Ashwin. Within-burst synchrony changes for coupled elliptic bursters. SIAM Journal on Applied Dynamical Systems 9:261-281 (2010) click here for pdf preprint

P. Ashwin and A. Goetz. Cone exchange transformations and boundedness of orbits. Ergodic Theory and Dynamical Systems (2010), appeared online (2009) doi:10.1017/S0143385709000625 click here for pdf preprint

P. Ashwin and A. Lavric. A low-dimensional model of binocular rivalry using winnerless competition. Physica D (2010), appeared online (2009) http://www.sciencedirect.com/scidirimg/clear.gifdoi:10.1016/j.physd.2009.06.018  click here for pdf preprint

2009

O. Karabacak and P. Ashwin. Heteroclinic Ratchets in a System of Four Coupled Oscillators. J Nonlinear Sci Vol 20, p105 (2010), on-lin (2009)  doi:10.1007/s00332-009-9053-2 http://arxiv.org/abs/0811.1012 click here for pdf preprint

P. Ashwin, X.-C. Fu and C. Lin. On planar piecewise and two-torus parabolic maps. Intl. J. Bifurcation and Chaos 19:2383-2390 (2009) click here for pdf preprint

G. Orosz, P. Ashwin and S.B. Townley, Learning of spatiotemporal codes in a coupled oscillator system. IEEE Transactions in Neural Networks http://dx.doi.org/10.1109/TNN.2009.2016658 (2009) click here for pdf preprint

G Orosz, J. Moehlis, P. Ashwin, Designing the Dynamics of Globally Coupled Oscillators. Progress of Theoretical Physics 122:611-630 (2009) http://ptp.ipap.jp/link?PTP/122/611/ click here for pdf preprint

2008

J. Wordsworth and P. Ashwin. Spatio-temporal coding of inputs for a system of globally coupled phase oscillators. Phys Rev E 78:066203 (2008) click here for pdf preprint

P. Ashwin, B.S.V. Patnaik, C.D. Wright. Fast simulation of phase-change processes in chalcogenide alloys using a Gillespie-type cellular automata approach, J Applied Phys,104, 084101 (2008). click here for pdf preprint

M. Trovati, P. Ashwin and N. Byott. Packings induced by piecewise isometries cannot contain the arbelos. Discrete and Continuous Dynamical Systems - A, 22(3), 791-806 (2008) click here for pdf preprint

P. Ashwin, O. Burylko and Y. Maistrenko. Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators. click here for pdf preprint Physica D 237:454-466 (2008), http://dx.doi.org/10.1016/j.physd.2007.09.015.


2007

P. Ashwin, G. Orosz, J. Wordsworth and S. Townley. Dynamics on Networks of Cluster States for Globally Coupled Phase Oscillators, SIAM J Applied Dynamical Systems 6:728-758 (2007). link to paper , click here for pdf preprint

G. Orosz, P. Ashwin, J. Wordsworth and S. Townley, Cluster synchronization, switching and spatio-temporal coding in a phase oscillator network. click here for pdf preprint PAMM, 7:1030703 - 1030704 (2007) (ICIAM07 Minisymposia - 03 Nonlinear Analysis and Dynamical Systems 2007)

C. D. Wright, P. Ashwin and K. Blyuss. Master equation approach to understanding multi-state phase-change memories and processors, Applied Physics Letters 90:063113 (2007). link to article  preprint

O. Podvigina and P. Ashwin. The sqrt(2):1 mode interaction and heteroclinic networks in Boussinesq convection. click here for pdf preprint Physica D 234, 23-48 (2007) http://dx.doi.org/10.1016/j.physd.2007.06.024

M. Trovati and P. Ashwin. Tangency properties of a pentagonal tiling generated by a piecewise isometry. Chaos 17:043129 (2007) click here for pdf preprint

2006

O. Podvigina, P. Ashwin and D.J. Hawker, Modelling instability of ABC flow using a mode interaction between steady and Hopf bifurcations with rotational symmetries of the cube. Physica D 215, 62-79 (2006). preprint

K. Blyuss, P. Ashwin, C.D. Wright and A. Bassom, Front propagation in a phase field model with phase-dependent heat absorption. Physica D 215, 127-136 (2006). click here for pdf preprint

P. Ashwin and A. Goetz. Polygonal invariant curves for a planar piecewise isometry. Trans AMS 348:373-390 (2006). click here for pdf preprint

P. Ashwin, O. Burylko, Y. Maistrenko and O. Popovych, Extreme sensitivity to detuning for globally coupled phase oscillators. Phys Rev Letts 96:054102 (2006). click here for pdf preprint

Peter Ashwin (2006) Bubbling transition. Scholarpedia, 1(8):1725

2005

D.J. Hawker and P. Ashwin. Bursting to the origin: a robust heteroclinic cycle including maximal symmetry equilibria. Intl. J. Bifurcation and Chaos 15 (2005) 2819-2832 click here for pdf preprint

P. Ashwin and G. Dangelmayr. On globally coupled weakly dissipative and strongly nonlinear oscillators. Dynamical Systems 20 (2005) 333-367 click here for pdf preprint

P. Ashwin and J. Borresen. Discrete computation using a perturbed heteroclinic network. Physics Letters A 347 (2005) 208-214 click here for pdf preprint  link to final version

D.J. Hawker and P. Ashwin. Classification of robust heteroclinic cycles for vector fields in R^3 with symmetry, J. Phys. A: Math. Gen. 38 (2005) 8319-8335 click here for pdf preprint

P. Ashwin and M. Timme. When instability makes sense. Nature 436:36-37 (2005)

P. Ashwin and M. Timme. Unstable attractors: existence and robustness in networks of oscillators with delayed pulse coupling. Nonlinearity 18 2035--2060 (2005) click here for pdf preprint  click here for link to final version

K.B. Blyuss, P. Ashwin, A.P. Bassom and C.D. Wright. Master equation approach to the study of phase change processes in data storage media. Phys Rev E 72 (2005) 011607 click here for pdf preprint

P. Ashwin and A. Goetz. Invariant curves and explosion of periodic islands for piecewise isometries. SIAM Journal of Applied Dynamical Systems. 4:437-458 (2005). click here for ps preprint

P. Ashwin. Riddled basins and coupled dynamical systems. (in "Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems", Eds: J-R Chazottes and B Fernandez, Springer Lecture Notes in Physics vol 671, 2005) click here for pdf preprint

2004

P. Ashwin, A.M. Rucklidge and R. Sturman. Cycling chaotic attractors in two models for dynamics with invariant subspaces. Chaos 14:571 (2004) click here for pdf preprint

P. Ashwin and M. Field. Product dynamics for homoclinic attractors. Proc Roy Soc A, vol 461, 155-177 (2004) click here for pdf preprint

R. Sturman and P. Ashwin. Internal dynamics of intermittency. In: Dynamics and Bifurcation of Patterns in Dissipative Systems, Eds: G. Dangelmayr and I. Oprea, World Scientific Series on Nonlinear Science {\bf 12}, World Scientific, Singapore, 2004. click here for pdf preprint

P. Ashwin, A.M. Rucklidge and R. Sturman. Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory. Physica D 194:30--48 (2004) click here for pdf preprint

P. Ashwin and J. Borresen. Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators. Phys. Rev. E 70:026203 (2004). click here for pdf preprint

2003

P. Ashwin, A. Rucklidge and R. Sturman. "Cycling attractors of coupled cell systems and dynamics with symmetry", In: Proceedings of Workshop on Synchronization, Crimea, 2002. Eds A. Pikovsky and Y. Maistrenko, Kluwer (2003) click here for pdf preprint

P. Ashwin, Xin-Chu Fu and J. Deane. Properties of the invariant disk packing in a model bandpass sigma-delta modulator. International Journal of Bifurcation and Chaos, 13:631 - 641 (2003). click here for pdf preprint

P. Ashwin and R. Sturman. Decelerating defects and non-ergodic critical behaviour in a unidirectionally coupled map lattice. Phys Letters A 309:423 - 434 (2003). click here for pdf preprint Link to article

P. Ashwin. Synchronization from chaos. `News and Views', Nature 422:384-385 (2003).

P. Ashwin. Patchwork patterns: dynamics on unbounded domains. Proceedings of workshop on Symmetry and Bifurcation, Porto 2000, Editors: J Buescu, S Castro, A Dias and I Laboriau (Birkhauser 2003). click here for pdf preprint

P. Ashwin and O. Podvigina. Hopf bifurcation with rotational symmetry of the cube and instability of ABC flow. Proc Roy Soc A 459:1801-1827 (2003). click here for pdf preprint

P. Ashwin and G. Ochs. Convergence and local random attractors. Dynamical Systems 18:139-158 (2003). click here for pdf preprint

P. Ashwin, M. Field, A.M. Rucklidge and R. Sturman. Phase resetting effects for robust cycles between chaotic sets. Chaos 13:973-981 (2003). click here for pdf preprint

Xin-Chu Fu and P. Ashwin. Symbolic analysis for some planar piecewise linear maps. Discrete and Continuous Dynamical Systems 9:1533-1548 (2003).

2002

P. Ashwin, and X.-C. Fu. On the dynamics of some nonhyperbolic area-preserving piecewise linear maps. Proceedings of 5th IMA conference on signal processing, Warwick, 2000. Edited by J. G. McWhirter and I. K. Proudler. The Institute of Mathematics and its Applications Conference Series. New Series, 71. The Clarendon Press, Oxford University Press, Oxford, (2002). click here for pdf preprint

P. Ashwin, A.M. Rucklidge and R. Sturman. Infinities of periodic orbits in systems of coupled oscillators. Phys. Rev. E 66:035201(R) (2002). click here for pdf preprint

P. Ashwin, M. Nicol and N. Kirkby. Acceleration of one dimensional mixing by discontinuous mappings. Physica A 310:347-363 (2002). click here for pdf preprint Link to article

P. Ashwin, X.-C. Fu and J.R. Terry. Riddling of invariant sets for some discontinuous maps preserving Lebesgue measure. Nonlinearity 15:633-645 (2002) click here for pdf preprint

P. Ashwin, M.V. Bartuccelli, T.J. Bridges and S.A. Gourley. Travelling fronts for the KPP equation with spatio-temporal delay. ZAMP 53:103-122, (2002). click here for pdf preprint

P. Ashwin and James Montaldi. Group theoretic conditions for existence of robust relative homoclinic trajectories. Math. Proc. Camb. Phil. Soc. 133:125-141, (2002). click here for pdf preprint

P. Ashwin and Xin-Chu Fu. On the geometry of orientation preserving planar piecewise isometries. Journal of Nonlinear Science 12:207-240 (2002). click here for pdf preprint

2001

P. Ashwin and M. Breakspear. Anisotropic properties of riddled basins. Physics Letters A 280:139--145 (2001) click here for pdf preprint

M. Nicol, I. Melbourne and P. Ashwin. Euclidean extensions of dynamical systems. Nonlinearity 14:275--300 (2001). click here for pdf preprint

P. Ashwin, I. Melbourne and M. Nicol. Hypermeander of spirals: local bifurcations and statistical properties Physica D 156:364--382 (2001). click here for pdf preprint

P. Ashwin, J.H.B. Deane and X.-C. Fu. Dynamics of a bandpass sigma-delta modulator as a piecewise isometry, Proceedings, ISCAS 2001}, (Proceedings of the IEEE International Symposium on Circuits and Systems, 2001), pp III-811 -- III-814 (Sydney, Australia, 2001). click here for pdf preprint

E. Covas, R. Tavakol, P. Ashwin, A. Tworkowski and J.M. Brooke. In-out intermittency in PDE and ODE models of axisymmetric mean field dynamos. Chaos 11:404-409 (2001). click here for pdf preprint

P. Ashwin and Xin-Chu Fu. Tangencies in invariant disk packings for certain planar piecewise isometries are rare. Dynamical Systems 16:333-345 (2001). click here for pdf preprint

P. Ashwin, E. Covas and R. Tavakol. Influence of noise on scalings for in-out intermittency. Physical Review E 64:066204 (2001). click here for pdf preprint

X.-C. Fu, W. Lu, P. Ashwin and J. Duan. Symbolic representation of Iterated Maps. Topological Methods in Nonlinear Analysis 18:119-147 (2001). click here for pdf preprint

2000

P. Ashwin, X-C Fu, T. Nishskawa and K. Zyczkowski. Invariant sets for discontinuous parabolic maps of the torus. Nonlinearity 13:819--835 (2000). click here for pdf preprint

P. Ashwin and J. Terry. On riddling and weak attractors. Physica D 142:87-100 (2000). click here for pdf preprint

J. Terry and P.Ashwin. Comment on ``Riddling of Chaotic Sets in Periodic Windows'' by Y-C Lai and C. Grebogi. Phys. Rev. Lett. 85:472-472 (2000).

P. Ashwin and G. Dangelmayr. Unfolding isochronicity in weakly dissipative coupled oscillators. Dynamics and Stability of Systems 15:263--286 (2000). click here for pdf preprint

P. Ashwin, I. Melbourne and M. Nicol. Drift for Euclidean extensions of dynamical systems. Proceedings of Equadiff 1999, Berlin (Eds: B. Fiedler, K. Groeger and J. Sprekels): pp 145--150. World Scientific, Singapore (2000). click here for pdf preprint

1999

P. Ashwin, Attractors of a randomly forced electronic oscillator. Physica D 125: 302--310 (1999). Click here for pdf preprint

J.R. Terry, K.S. Thornburg Jr., D.J. DeShazer, G.D. VanWiggeren, R. Roy, P. Ashwin and S. Zhu, Synchronization of Chaos in an Array of Three Lasers. Physical Review E 59:4036--4043 (1999) click here for pdf preprint

P. Ashwin, E. Covas & R. Tavakol, Transverse instability for non-normal parameters. Nonlinearity 12:563--577 (1999). click here for pdf preprint

P. Ashwin, I. Melbourne and M. Nicol, Drift bifurcations of relative equilibria and transitions of spiral waves. Nonlinearity 12:741--755 (1999) click here for pdf preprint

P. Ashwin Minimal attractors and bifurcations of random dynamical systems. Proc. Roy. Soc. London A 455:2615--2634 (1999) Click here for pdf preprint

P. Ashwin Chaotic intermittency of patterns in symmetric systems. Proceedings of IMA workshop on pattern formation in coupled and continuous systems Editors: M Golubitsky, D Luss and S H Strogatz, IMA volumes in Mathematics and its applications 115, Springer (1999). Click here for pdf preprint

P. Ashwin and M.J. Field, Heteroclinic networks in coupled cell systems. Arch. Rational Mech. Anal. 148:107--143 (1999). Click here for pdf preprint

J.H.B. Deane, P. Ashwin, D.C. Hamill and D.J. Jefferies. Calculation of spectral peaks in a chaotic dc-dc converter. IEEE Trans Circuits and Systems 46:1313-1319 (1999). click here for pdf preprint

1998

P. Ashwin, P.J. Aston and M. Nicol, On the unfolding of a blowout bifurcation. Physica D, 111:81-95 (1998). click here for pdf preprint

P. Ashwin and P. Chossat, Attractors for robust heteroclinic cycles with continua of connections. J. Nonlin. Sci, 8:103-129 (1998). click here for pdf preprint

P. Ashwin, W.G. Chambers and G. Petkov, Lossless digital filter overflow oscillations; approximation of invariant fractals. Intl. J. Bifurcation and Chaos, 7:2603-2610 (1997). click here for pdf preprint

P. Ashwin & P.J. Aston, Blowout bifurcations of codimension two. Physics Letters A 244:261-270 (1998).

P. Ashwin and A.M. Rucklidge, Cycling chaos; its creation, persistence and loss of stability in a model of nonlinear magnetoconvection. Physica D, 122:134-154 (1998). click here for pdf preprint

P. Ashwin and Mei Zhen, A numerical bifurcation function for homoclinic orbits. SIAM J. Numer. Anal., 35:2055-2069 (1998). click here for pdf preprint

P. Ashwin, Boundary of two-frequency behaviour in a system of three weakly coupled electronic oscillators. Chaos, Solitons and Fractals, 9:1279-1287 (1998). Click here for pdf preprint

P. Ashwin, J. Terry, K.S. Thornburg Jr & R. Roy. Blowout bifurcation in a system of coupled chaotic lasers. Phys Rev E, 6:7186-7189 (1998). Click here for pdf preprint

P. Ashwin. Nonlinear dynamics, loss of synchronization and symmetry breaking. Proc Instn Mech Engrs 212: 183--187 (1998). Click here for pdf preprint

1997

P. Ashwin, Elliptic behaviour in the sawtooth standard map. Physics Letters A, 232:409-416 (1997). click here for pdf preprint

P. Ashwin and E. Stone, On the influence of noise near blowout bifurcation. Phys Rev E, 56:1635-1641 (1997).

E. Covas, P. Ashwin and R. Tavakol, Non-normal parameter blowout bifurcation in a truncated mean field dynamo. Phys Rev E, 56:6451-6458 (1997).

P. Ashwin and M. Nicol, Detecting symmetries from observations. Part I: Theory. Physica D 100:58-70 (1997).

P. Ashwin and J. Tomes, Detecting symmetries from observations. Part II: An experiment with $S_4$ symmetry. Physica D 100:71-84 (1997).

P. Ashwin and G.P. King, A study of particle paths in non-axisymmetric Taylor-Couette flows. Journal of Fluid Mechanics 338:341-362 (1997). preprint

P. Ashwin and I. Melbourne Noncompact drift for relative equilibria and relative periodic orbits. Nonlinearity 10:595-616 (1997).

P. Ashwin, Cycles homoclinic to chaotic sets; robustness and resonance. Chaos, 7:207-220 (1997). click here for pdf preprint

1996

D. Aronson, M. Krupa and P. Ashwin, Semirotors in the Josephson junction equations, Journal of Nonlinear Science, 6(1):85-103 (1996).

P. Ashwin, J. Buescu and I. Stewart, From attractor to chaotic saddle: a tale of transverse instability, Nonlinearity 9:703-737 (1996). preprint

P. Ashwin, Mei Zhen and K. Boehmer, Forced symmetry breaking of homoclinic cycles in a PDE with O(2) symmetry. Journal of Computational and Applied Math. 70:297-310 (1996).

P. Ashwin, Non-smooth invariant circles in digital overflow oscillations. In: NDES96: proceedings of the fourth international workshop on Nonlinear Dynamics of Electronic Systems, Seville pp417-422 (1996).

1995

P. Ashwin, I. Moroz and R.M. Roberts, Bifurcation of stationary, standing and travelling waves in triply diffusive convection, Physica D 81:374-397 (1995).

P. Ashwin and G.P. King, Streamline topology in eccentric Taylor vortex flow, Journal of Fluid Mechanics 285:215-247 (1995). (with appendix B by G. Rowlands)

P. Ashwin, K. Boehmer and Mei Zhen, A numerical Liapunov-Schmidt reduction with applications to Hopf bifurcation on a square, Mathematics of Computation 64:649-670, and supplement pp. 19-22 (1995).

P. Ashwin and J.W. Swift, Torus doubling in four weakly coupled oscillators, International Journal of Bifurcation and Chaos 5:231-241 (1995).

P. Ashwin and Mei Zhen, Normal form for Hopf bifurcation of PDEs on the square, Nonlinearity 8:715-734 (1995). preprint

P. Ashwin, Weak coupling of strongly nonlinear, weakly dissipative identical oscillators, Dynamics and Stability of Systems 10:203-216 (1995). preprint

P. Ashwin Attractors stuck on to invariant subspaces. Physics Letters A 209:338-344 (1995).

P. Ashwin, G.P. King and G. Mann, Azimuthally progagating ring vortices in a model for nonaxisymmetric Taylor vortex flow, Physical Review Letters 75(25):4610-4613 (1995).

P. Ashwin, Symmetric dynamics in electronic circuits, In Nonlinear dynamics in circuits, Eds. T. Carroll and L. Pecora, World Scientific (Singapore) 1995.

1994

P. Ashwin and I. Melbourne, Symmetry groups of attractors, Arch. Rat. Mech. Anal. 126:59-78 (1994).

P. Ashwin and J.W. Swift, Measuring rotation sets of weakly coupled oscillators, Nonlinearity 7:925-942 (1994). preprint

P. Ashwin, P. Chossat and I. Stewart, Transitivity of orbits of maps symmetric under compact Lie groups, Chaos, Solitons and Fractals 4:621-634 (1994). Correction: Chaos Solitons and Fractals 5:131 (1995).

P. Ashwin, G. Dangelmayr, I. Stewart and M. Wegelin, Oscillator networks with the symmetry of the unit quaternions, in proceedings of Dynamics, Bifurcations and symmetry, Cargese, Kluwer (Dordrecht), pp. 35-48 (1994). preprint

P. Ashwin and P. Stork, Permissible symmetries of coupled cell networks, Math. Proc. Camb. Phil. Soc. 116:27-36 (1994).

P. Ashwin, J. Buescu and I. Stewart, Bubbling of attractors and synchronisation of chaotic oscillators, Physics Letters A 193:126-139 (1994). preprint

P. Ashwin and Mei Zhen, A Hopf bifurcation with Robin boundary conditions, Journal of Dynamics and Differential Equations 6:487-503 (1994).

P. Ashwin, G. Ikegami, G.P. King, J. Nijhof and K. Tchizawa, Simulation of an electronic multivibrator, Geometry and analysis in dynamical systems (Kyoto 1993), 13-28, Advanced Series in Dynamical Systems 14, World. Sci. Publishing, River Edge, NJ (1994).

1993

P. Ashwin, J. Guaschi and J.M. Phelps, Rotation sets and phase-locking in an electronic three oscillator system, Physica D 66:392-411 (1993).

P. Ashwin and J.W. Swift, Unfolding the torus: oscillator geometry from time delays, Journal of Nonlinear Science 3:459-475 (1993).

P. Ashwin, K. Boehmer and Mei Zhen, A numerical Liapunov-Schmidt method for finitely determined problems, Exploiting symmetry in applied and numerical analysis eds E.L. Allgower, J.K. Georg and R. Miranda, AMS Lectures in Applied Mathematics vol. 29, pp 49-70 (1993).

E. Allgower, P. Ashwin, K. Boehmer and Mei Zhen, Liapunov-Schmidt reduction for a bifurcation problem with periodic boundary conditions on a square domain, Exploiting symmetry in applied and numerical analysis eds E.L. Allgower, J.K. Georg and R. Miranda, AMS Lectures in Applied Mathematics vol. 29, pp 11-22 (1993).

1992

P. Ashwin and J.W. Swift, The dynamics of $n$ identical oscillators with symmetric coupling. Journal of Nonlinear Science 2:69-108 (1992). preprint

P. Ashwin, Identical oscillator networks with symmetry, in proceedings of Coupled oscillating neurons, London, December 1990, Perspectives in Neural Computing, eds. J. Taylor and C. Mannion, Springer pp 21-40 (1992).

P. Ashwin, High corank steady-state mode interactions on a rectangle, in proceedings of Bifurcation and symmetry, Marburg 1991, eds E. Allgower, K. Boehmer and M. Golubitsky, Birkhaeuser Verlag, Basel, pp 23-33 (1992).

1990

P. Ashwin, G.P. King and J.W. Swift, Three identical coupled oscillators with symmetry, Nonlinearity 3:585-603 (1990). preprint 

P. Ashwin, Symmetric chaos in systems of three and four coupled oscillators, Nonlinearity 3:604-618 (1990).

Preprints

P. Ashwin and I. Melbourne. Dynamics on unbounded domains; co-solutions and inheritance of stability. click here for pdf preprint

P. Ashwin, S. Wieczorek, R. Vitolo and P. Cox. Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system. arXiv:1103.0169v2 

C. Lin, G. Steinberg and P. Ashwin, Bidirectional transport and pulsing states in a multi-lane ASEP model. http://arxiv.org/abs/1104.5090

C. Bick, M. Timme, D. Paulikat, D. Rathlev and P. Ashwin, Chaos in Symmetric Oscillator Networks. http://arxiv.org/abs/1105.2230

Other publications

P. Ashwin and B. Mestel. Mathematics; history and culture. LTSN MSOR connections vol 3 no 3:21-23 (2003).


P.Ashwin@ex.ac.uk
Last modified: 28th June 2011