doi:10.1016/j.physd.2009.06.018
click
here for pdf preprintM. 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
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) doi: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).
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).
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).
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/1104.5090P. Ashwin and B. Mestel. Mathematics; history
and culture. LTSN MSOR
connections vol 3 no 3:21-23 (2003).