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## Ashwin, Peter

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 Author ID: ashwin.peter Published as: Ashwin, P.; Ashwin, Peter External Links: ORCID
 Documents Indexed: 125 Publications since 1990
all top 5

#### Co-Authors

 11 single-authored 9 Fu, Xinchu 7 Mei, Zhen 7 Nicol, Matthew 7 Sturman, Rob 6 Melbourne, Ian 5 Podvigina, Ol’ga Mikhaĭlovna 5 Rucklidge, Alastair M. 5 Stewart, Ian Nicholas 5 Swift, James W. 4 Böhmer, Klaus 4 Field, Michael J. 4 Goetz, Arek 4 Karabacak, Özkan 4 King, Gregory P. 3 Chossat, Pascal 3 Dangelmayr, Gerhard 3 Hawker, David 3 Orosz, Gábor 3 Postlethwaite, Claire M. 3 Rodrigues, Ana 3 Terry, John R. 3 Tsaneva-Atanasova, Krasimira T. 3 Wieczorek, Sebastian M. 2 Aston, Philip J. 2 Bick, Christian 2 Borresen, Jon 2 Buescu, Jorge 2 Burylko, Oleksandr 2 Cox, Peter M. 2 Creaser, Jennifer L. 2 Luke, C. M. 2 Trovati, Marcello 1 Aguiar, Manuela A. D. 1 Alkhayuon, Hassan M. 1 Allgower, Eugene L. 1 Aronson, Donald G. 1 Azad, Abul Kalam Al 1 Bartuccelli, Michele V. 1 Bassom, Andrew P. 1 Benjamin, Oscar 1 Blyuss, Konstantin B. 1 Breakspear, Michael 1 Bridges, Thomas J. 1 Broomhead, David S. 1 Byott, Nigel P. 1 Callard, Robin E. 1 Castro, Sofia B. S. D. 1 Chambers, William G. 1 Chawanya, Tsuyoshi 1 Chowdhury, Fahmida N. 1 Coombes, Stephen 1 Covas, Eurico O. 1 Deane, Jonathan H. B. 1 Dias, Ana Paula S. 1 Duan, Jinqiao 1 Fitzgerald, Thomas H. B. 1 Glendinning, Paul Alexander 1 Gourley, Stephen A. 1 Guaschi, John 1 Huguet, Gemma 1 Ikegami, Giko 1 Ismail, Asma 1 Krupa, Martin 1 Lavric, Aureliu 1 Lin, Congping 1 Lohse, Alexander 1 Lu, Weiping 1 Maistrenko, Yuri L. 1 Moehlis, Jeff 1 Montaldi, James A. 1 Moroz, Irene M. 1 Nicks, Rachel 1 Nijhof, J. H. B. 1 Nishikawa, Takashi 1 Nowotny, Thomas 1 Ochs, Gunter 1 Peres, Pedro L. D. 1 Pérez-Cervera, Alberto 1 Perryman, Clare 1 Petkov, Georgi P. 1 Phelps, J. M. 1 Rankin, James 1 Richardson, Mark P. 1 Roberts, Richard Mark 1 Roslan, Ummu Atiqah Mohd 1 M-Seara, Tere 1 Smug, Damian 1 Sornette, Didier 1 Stork, Peter C. 1 Tavakol, Reza 1 Tchizawa, Koyoyuki 1 Thoubaan, Mary 1 Timme, Marc 1 Tomes, Jörg 1 Townley, Stuart B. 1 von der Heydt, Anna S. 1 Wegelin, Michael 1 Weinberger, Oskar 1 Wordsworth, John 1 Wright, C. David ...and 1 more Co-Authors
all top 5

#### Serials

 17 Physica D 15 Nonlinearity 9 Journal of Nonlinear Science 9 Chaos 7 Dynamical Systems 6 Physics Letters. A 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 SIAM Journal on Applied Dynamical Systems 5 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 The Journal of Mathematical Neuroscience 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Chaos, Solitons and Fractals 2 Archive for Rational Mechanics and Analysis 2 Journal of Fluid Mechanics 2 Ergodic Theory and Dynamical Systems 2 Dynamics and Stability of Systems 2 Discrete and Continuous Dynamical Systems 1 Journal of Statistical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics of Computation 1 Journal of Computational and Applied Mathematics 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Journal of Physics A: Mathematical and General 1 Journal of Dynamics and Differential Equations 1 Topological Methods in Nonlinear Analysis 1 Discrete and Continuous Dynamical Systems. Series B 1 Progress of Theoretical Physics
all top 5

#### Fields

 97 Dynamical systems and ergodic theory (37-XX) 47 Ordinary differential equations (34-XX) 13 Partial differential equations (35-XX) 12 Biology and other natural sciences (92-XX) 9 Numerical analysis (65-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Fluid mechanics (76-XX) 6 Information and communication theory, circuits (94-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Probability theory and stochastic processes (60-XX) 3 Geophysics (86-XX) 2 Computer science (68-XX) 2 Mechanics of particles and systems (70-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX)

#### Citations contained in zbMATH Open

115 Publications have been cited 1,175 times in 690 Documents Cited by Year
From attractor to chaotic saddle: A tale of transverse instability. Zbl 0887.58034
Ashwin, Peter; Buescu, Jorge; Stewart, Ian
1996
The dynamics of $$n$$ weakly coupled identical oscillators. Zbl 0872.58049
Ashwin, P.; Swift, J. W.
1992
Travelling fronts for the KPP equation with spatio-temporal delay. Zbl 1005.92024
Ashwin, P.; Bartuccelli, M. V.; Bridges, T. J.; Gourley, S. A.
2002
Bubbling of attractors and synchronisation of chaotic oscillators. Zbl 0959.37508
Ashwin, Peter; Buescu, Jorge; Stewart, Ian
1994
Mathematical frameworks for oscillatory network dynamics in neuroscience. Zbl 1356.92015
Ashwin, Peter; Coombes, Stephen; Nicks, Rachel
2016
Heteroclinic networks in coupled cell systems. Zbl 0947.37012
Ashwin, Peter; Field, Michael
1999
Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation. Zbl 1254.37053
Aguiar, M.; Ashwin, P.; Dias, A.; Field, M.
2011
Weak chimeras in minimal networks of coupled phase oscillators. Zbl 1345.34052
Ashwin, Peter; Burylko, Oleksandr
2015
Three identical oscillators with symmetric coupling. Zbl 0708.58020
Ashwin, Peter; King, G. P.; Swift, James W.
1990
Dynamics on networks of cluster states for globally coupled phase oscillators. Zbl 1167.34326
Ashwin, Peter; Orosz, Gábor; Wordsworth, John; Townley, Stuart
2007
On designing heteroclinic networks from graphs. Zbl 1417.37098
Ashwin, Peter; Postlethwaite, Claire
2013
On local attraction properties and a stability index for heteroclinic connections. Zbl 1219.37021
Podvigina, Olga; Ashwin, Peter
2011
Elliptic behaviour in the sawtooth standard map. Zbl 1053.37520
Ashwin, Peter
1997
Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators. Zbl 1178.34041
Ashwin, Peter; Burylko, Oleksandr; Maistrenko, Yuri
2008
Noncompact drift for relative equilibria and relative periodic orbits. Zbl 0912.35079
Ashwin, Peter; Melbourne, Ian
1997
Lossless digital filter overflow oscillations; approximation of invariant fractals. Zbl 0902.65100
Ashwin, Peter; Chambers, W.; Petkov, G.
1997
On the geometry of orientation-preserving planar piecewise isometries. Zbl 1100.37027
Ashwin, P.; Fu, X.-C.
2002
Unstable attractors: existence and robustness in networks of oscillators with delayed pulse coupling. Zbl 1084.37061
Ashwin, Peter; Timme, Marc
2005
Transverse instability for non-normal parameters. Zbl 0984.37053
Ashwin, Peter; Covas, Eurico; Tavakol, Reza
1999
Tangencies in invariant disc packings for certain planar piecewise isometries are rare. Zbl 1032.37026
Ashwin, Peter; Fu, Xin-Chu
2001
Attractors for robust heteroclinic cycles with continua of connections. Zbl 0901.58045
Ashwin, P.; Chossat, P.
1998
Chaotic weak chimeras and their persistence in coupled populations of phase oscillators. Zbl 1355.37041
Bick, Christian; Ashwin, Peter
2016
Excitability in ramped systems: the compost-bomb instability. Zbl 1219.86006
Wieczorek, S.; Ashwin, P.; Luke, C. M.; Cox, P. M.
2011
Parameter shifts for nonautonomous systems in low dimension: bifurcation- and rate-induced tipping. Zbl 1435.37104
Ashwin, Peter; Perryman, Clare; Wieczorek, Sebastian
2017
Polygonal invariant curves for a planar piecewise isometry. Zbl 1080.37009
Ashwin, Peter; Goetz, Arek
2006
Discrete computation using a perturbed heteroclinic network. Zbl 1195.34053
Ashwin, Peter; Borresen, Jon
2005
Invariant curves and explosion of periodic islands in systems of piecewise rotations. Zbl 1090.37029
Ashwin, Peter; Goetz, Arek
2005
Symbolic analysis for some planar piecewise linear maps. Zbl 1042.37009
Fu, Xin-Chu; Ashwin, Peter
2003
Riddling and invariance for discontinuous maps preserving Lebesgue measure. Zbl 1073.37009
Ashwin, Peter; Fu, Xin-Chu; Terry, John R.
2002
Euclidean extensions of dynamical systems. Zbl 1183.37043
Nicol, Matthew; Melbourne, Ian; Ashwin, Peter
2001
On riddling and weak attractors. Zbl 0954.37015
Ashwin, Peter; Terry, John R.
2000
Hopf normal form with $$S_N$$ symmetry and reduction to systems of nonlinearly coupled phase oscillators. Zbl 1364.34041
Ashwin, Peter; Rodrigues, Ana
2016
Criteria for robustness of heteroclinic cycles in neural microcircuits. Zbl 1259.37054
Ashwin, Peter; Karabacak, Özkan; Nowotny, Thomas
2011
Designing the dynamics of globally coupled oscillators. Zbl 1196.34046
Orosz, Gábor; Moehlis, Jeff; Ashwin, Peter
2009
Hopf bifurcation with cubic symmetry and instability of ABC flow. Zbl 1116.37310
Ashwin, Peter; Podvigina, Olga
2003
Symmetric chaos in systems of three and four forced oscillators. Zbl 0711.94031
Ashwin, Peter
1990
Chaos in generically coupled phase oscillator networks with nonpairwise interactions. Zbl 1382.34038
Bick, Christian; Ashwin, Peter; Rodrigues, Ana
2016
Properties of the invariant disk packing in a model bandpass sigma-delta modulator. Zbl 1056.37059
Ashwin, Peter; Fu, Xin-Chu; Deane, Jonathan
2003
On the unfolding of a blowout bifurcation. Zbl 0930.37013
Ashwin, Peter; Aston, Philip J.; Nicol, Matthew
1998
Symbolic representations of iterated maps. Zbl 1021.37007
Fu, Xin-Chu; Lu, Weiping; Ashwin, Peter; Duan, Jinqiao
2001
A Hopf bifurcation with Robin boundary conditions. Zbl 0807.35013
Ashwin, Peter; Mei, Zhen
1994
Symmetry groups of attractors. Zbl 0817.58020
Ashwin, Peter; Melbourne, Ian
1994
A study of particle paths in non-axisymmetric Taylor-Couette flows. Zbl 0889.76089
Ashwin, P.; King, G. P.
1997
A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy. Zbl 1291.92022
Benjamin, Oscar; Fitzgerald, Thomas H. B.; Ashwin, Peter; Tsaneva-Atanasova, Krasimira; Chowdhury, Fahmida; Richardson, Mark P.; Terry, John R.
2012
Heteroclinic ratchets in networks of coupled oscillators. Zbl 1208.34057
Karabacak, Özkan; Ashwin, Peter
2010
Cycling chaos: Its creation, persistence and loss of stability in a model of nonlinear magnetoconvection. Zbl 0955.76035
Ashwin, Peter; Rucklidge, A. M.
1998
Rate-induced tipping from periodic attractors: partial tipping and connecting orbits. Zbl 1392.37026
Alkhayuon, Hassan M.; Ashwin, Peter
2018
Designing heteroclinic and excitable networks in phase space using two populations of coupled cells. Zbl 1362.37058
Ashwin, Peter; Postlethwaite, Claire
2016
Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory. Zbl 1051.37041
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob
2004
Phase resetting effects for robust cycles between chaotic sets. Zbl 1080.37518
Ashwin, Peter; Field, Michael; Rucklidge, Alastair M.; Sturman, Rob
2003
On the dynamics of some nonhyperbolic area-preserving piecewise linear maps. Zbl 1013.37039
Ashwin, Peter; Fu, Xin-Chu
2002
Attractors of a randomly forced electronic oscillator. Zbl 1065.94567
Ashwin, Peter
1999
Torus doubling in four weakly coupled oscillators. Zbl 0885.58056
Ashwin, Peter; Swift, James W.
1995
Normal form for Hopf bifurcation of partial differential equations on the square. Zbl 0839.35010
Ashwin, Peter; Mei, Z.
1995
A numerical Liapunov-Schmidt method with applications to Hopf bifurcation on a square. Zbl 0829.65075
Ashwin, Peter; Böhmer, Klaus; Mei, Zhen
1995
Within-burst synchrony changes for coupled elliptic bursters. Zbl 1195.37032
Azad, Abul Kalam Al; Ashwin, Peter
2010
The $$1:\sqrt 2$$ mode interaction and heteroclinic networks in Boussinesq convection. Zbl 1141.76453
Podvigina, Olga; Ashwin, Peter
2007
Convergence to local random attractors. Zbl 1136.37345
Ashwin, Peter; Ochs, Gunter
2003
Drift bifurcations of relative equilibria and transitions of spiral waves. Zbl 0958.37017
Ashwin, Peter; Melbourne, Ian; Nicol, Matthew
1999
Boundary of two frequency behaviour in a system of three weakly coupled electronic oscillators. Zbl 0956.37013
Ashwin, Peter
1998
Streamline topology in eccentric Taylor vortex flow. Zbl 0882.76097
Ashwin, P.; King, G. P.
1995
High corank steady-state mode interactions on a rectangle. Zbl 0769.35006
Ashwin, Peter
1992
From coupled networks of systems to networks of states in phase space. Zbl 1395.37061
Weinberger, Oskar; Ashwin, Peter
2018
Quantifying noisy attractors: from heteroclinic to excitable networks. Zbl 1360.37141
Ashwin, Peter; Postlethwaite, Claire
2016
A low-dimensional model of binocular rivalry using winnerless competition. Zbl 1194.91167
Ashwin, Peter; Lavric, Aureliu
2010
Tangency properties of a pentagonal tiling generated by a piecewise isometry. Zbl 1163.37379
Trovati, Marcello; Ashwin, Peter
2007
Hypermeander of spirals: local bifurcations and statistical properties. Zbl 1049.92001
Ashwin, P.; Melbourne, I.; Nicol, M.
2001
Invariant sets for discontinuous parabolic area-preserving torus maps. Zbl 0952.37007
Ashwin, Peter; Fu, Xin-Chu; Nishikawa, Takashi; Życzkowski, Karol
2000
Minimal attractors and bifurcations of random dynamical systems. Zbl 0934.37049
Ashwin, Peter
1999
Detection of symmetry of attractors from observations. I: Theory. Zbl 0894.58037
Ashwin, Peter; Nicol, Matthew
1997
Semirotors in the Josephson junction equations. Zbl 0843.34041
Aronson, D. G.; Krupa, M.; Ashwin, P.
1996
Permissible symmetries of coupled cell networks. Zbl 0816.58035
Ashwin, Peter; Stork, Peter
1994
A numerical Liapunov-Schmidt method for finitely determined problems. Zbl 0787.58044
Ashwin, P.; Böhmer, K.; Mei, Z.
1993
Rotation sets and phase-locking in an electronic three oscillator system. Zbl 0784.34027
Ashwin, Peter; Guaschi, John; Phelps, J. M.
1993
Local and global stability indices for a riddled basin attractor of a piecewise linear map. Zbl 1370.37057
Roslan, Ummu Atiqah Mohd; Ashwin, Peter
2016
Robust heteroclinic behaviour, synchronization, and ratcheting of coupled oscillators. Zbl 1266.34059
Ashwin, Peter; Karabacak, Özkan
2011
On statistical attractors and the convergence of time averages. Zbl 1214.37024
Karabacak, Özkan; Ashwin, Peter
2011
Noise-induced switching near a depth two heteroclinic network and an application to Boussinesq convection. Zbl 1311.37013
Ashwin, Peter; Podvigina, Olga
2010
On planar piecewise and two-torus parabolic maps. Zbl 1176.37017
Ashwin, Peter; Fu, Xinchu; Lin, Congping
2009
Modelling instability $$ABC$$ flow using a mode interaction between steady and Hopf bifurcations with rotational symmetries of the cube. Zbl 1091.35520
Podvigina, Olga; Ashwin, Peter; Hawker, David
2006
Product dynamics for homoclinic attractors. Zbl 1145.37307
Ashwin, Peter; Field, Michael
2005
Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators. Zbl 1086.37041
Ashwin, P.; Dangelmayr, G.
2005
Isochronicity-induced bifurcations in systems of weakly dissipative coupled oscillators. Zbl 0976.34033
Ashwin, Peter; Dangelmayr, Gerhard
2000
Cycles homoclinic to chaotic sets; robustness and resonance. Zbl 1012.37020
Ashwin, Peter
1997
Forced symmetry breaking of homoclinic cycles in a PDE with O(2) symmetry. Zbl 0858.65123
Ashwin, Peter; Böhmer, Klaus; Mei, Z.
1996
Bifurcations of stationary, standing and travelling waves in triply diffusive convection. Zbl 0899.76165
Ashwin, Peter; Moroz, Irene; Roberts, Mark
1995
Unfolding the torus: Oscillator geometry from time delays. Zbl 0804.34036
Ashwin, P.; Swift, J. W.
1993
Existence and stability of Chimera states in a minimal system of phase oscillators. Zbl 1400.34059
Thoubaan, Mary; Ashwin, Peter
2018
Sequential noise-induced escapes for oscillatory network dynamics. Zbl 1387.60088
Creaser, Jennifer; Tsaneva-Atanasova, Krasimira; Ashwin, Peter
2018
Heteroclinic switching in coupled oscillator networks: dynamics on odd graphs. Zbl 1221.37044
Ashwin, Peter; Orosz, Gábor; Borresen, Jon
2010
Cone exchange transformations and boundedness of orbits. Zbl 1213.37063
Ashwin, Peter; Goetz, Arek
2010
Packings induced by piecewise isometries cannot contain the Arbelos. Zbl 1156.52013
Trovati, Marcello; Ashwin, Peter; Byott, Nigel
2008
Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria. Zbl 1093.37509
Hawker, David; Ashwin, Peter
2005
Cycling chaotic attractors in two models for dynamics with invariant subspaces. Zbl 1080.37026
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob
2004
Group theoretic conditions for existence of robust relative homoclinic trajectories. Zbl 1039.37015
Ashwin, Peter; Montaldi, James
2002
Chaotic intermittency of patterns in symmetric systems. Zbl 0999.37033
Ashwin, Peter
1999
Blowout bifurcations of codimension two. Zbl 1044.37515
Ashwin, Peter; Aston, Philip J.
1998
Oscillator networks with the symmetry of the unit quaternion group. Zbl 0817.58036
Ashwin, Peter; Dangelmayr, Gerhard; Stewart, Ian; Wegelin, Michael
1994
Liapunov-Schmidt reduction for a bifurcation problem with periodic boundary conditions on a square domain. Zbl 0787.58043
Allgower, E.; Ashwin, P.; Böhmer, K.; Mei, Z.
1993
Extreme sensitivity and climate tipping points. Zbl 1446.37075
Ashwin, Peter; von der Heydt, Anna S.
2020
Extreme sensitivity and climate tipping points. Zbl 1446.37075
Ashwin, Peter; von der Heydt, Anna S.
2020
Almost complete and equable heteroclinic networks. Zbl 1431.34058
Ashwin, Peter; Castro, Sofia B. S. D.; Lohse, Alexander
2020
The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability. Zbl 1439.92051
Pérez-Cervera, Alberto; Ashwin, Peter; Huguet, Gemma; Seara, Tere M.; Rankin, James
2019
Rate-induced tipping from periodic attractors: partial tipping and connecting orbits. Zbl 1392.37026
Alkhayuon, Hassan M.; Ashwin, Peter
2018
From coupled networks of systems to networks of states in phase space. Zbl 1395.37061
Weinberger, Oskar; Ashwin, Peter
2018
Existence and stability of Chimera states in a minimal system of phase oscillators. Zbl 1400.34059
Thoubaan, Mary; Ashwin, Peter
2018
Sequential noise-induced escapes for oscillatory network dynamics. Zbl 1387.60088
Creaser, Jennifer; Tsaneva-Atanasova, Krasimira; Ashwin, Peter
2018
A generalized 2D-dynamical mean-field Ising model with a rich set of bifurcations (inspired and applied to financial crises). Zbl 1392.37098
Smug, Damian; Sornette, Didier; Ashwin, Peter
2018
Parameter shifts for nonautonomous systems in low dimension: bifurcation- and rate-induced tipping. Zbl 1435.37104
Ashwin, Peter; Perryman, Clare; Wieczorek, Sebastian
2017
Mathematical frameworks for oscillatory network dynamics in neuroscience. Zbl 1356.92015
Ashwin, Peter; Coombes, Stephen; Nicks, Rachel
2016
Chaotic weak chimeras and their persistence in coupled populations of phase oscillators. Zbl 1355.37041
Bick, Christian; Ashwin, Peter
2016
Hopf normal form with $$S_N$$ symmetry and reduction to systems of nonlinearly coupled phase oscillators. Zbl 1364.34041
Ashwin, Peter; Rodrigues, Ana
2016
Chaos in generically coupled phase oscillator networks with nonpairwise interactions. Zbl 1382.34038
Bick, Christian; Ashwin, Peter; Rodrigues, Ana
2016
Designing heteroclinic and excitable networks in phase space using two populations of coupled cells. Zbl 1362.37058
Ashwin, Peter; Postlethwaite, Claire
2016
Quantifying noisy attractors: from heteroclinic to excitable networks. Zbl 1360.37141
Ashwin, Peter; Postlethwaite, Claire
2016
Local and global stability indices for a riddled basin attractor of a piecewise linear map. Zbl 1370.37057
Roslan, Ummu Atiqah Mohd; Ashwin, Peter
2016
Weak chimeras in minimal networks of coupled phase oscillators. Zbl 1345.34052
Ashwin, Peter; Burylko, Oleksandr
2015
Multi-cluster dynamics in coupled phase oscillator networks. Zbl 1351.37206
Ismail, Asma; Ashwin, Peter
2015
On designing heteroclinic networks from graphs. Zbl 1417.37098
Ashwin, Peter; Postlethwaite, Claire
2013
A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy. Zbl 1291.92022
Benjamin, Oscar; Fitzgerald, Thomas H. B.; Ashwin, Peter; Tsaneva-Atanasova, Krasimira; Chowdhury, Fahmida; Richardson, Mark P.; Terry, John R.
2012
Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation. Zbl 1254.37053
Aguiar, M.; Ashwin, P.; Dias, A.; Field, M.
2011
On local attraction properties and a stability index for heteroclinic connections. Zbl 1219.37021
Podvigina, Olga; Ashwin, Peter
2011
Excitability in ramped systems: the compost-bomb instability. Zbl 1219.86006
Wieczorek, S.; Ashwin, P.; Luke, C. M.; Cox, P. M.
2011
Criteria for robustness of heteroclinic cycles in neural microcircuits. Zbl 1259.37054
Ashwin, Peter; Karabacak, Özkan; Nowotny, Thomas
2011
Robust heteroclinic behaviour, synchronization, and ratcheting of coupled oscillators. Zbl 1266.34059
Ashwin, Peter; Karabacak, Özkan
2011
On statistical attractors and the convergence of time averages. Zbl 1214.37024
Karabacak, Özkan; Ashwin, Peter
2011
Correction to: “Excitability in ramped systems: the compost-bomb instability”. Zbl 1221.86005
Wieczorek, S.; Ashwin, P.; Luke, C. M.; Cox, P. M.
2011
Heteroclinic ratchets in networks of coupled oscillators. Zbl 1208.34057
Karabacak, Özkan; Ashwin, Peter
2010
Within-burst synchrony changes for coupled elliptic bursters. Zbl 1195.37032
Azad, Abul Kalam Al; Ashwin, Peter
2010
A low-dimensional model of binocular rivalry using winnerless competition. Zbl 1194.91167
Ashwin, Peter; Lavric, Aureliu
2010
Noise-induced switching near a depth two heteroclinic network and an application to Boussinesq convection. Zbl 1311.37013
Ashwin, Peter; Podvigina, Olga
2010
Heteroclinic switching in coupled oscillator networks: dynamics on odd graphs. Zbl 1221.37044
Ashwin, Peter; Orosz, Gábor; Borresen, Jon
2010
Cone exchange transformations and boundedness of orbits. Zbl 1213.37063
Ashwin, Peter; Goetz, Arek
2010
A minimal system with a depth-two heteroclinic network. Zbl 1204.37027
Chawanya, Tsuyoshi; Ashwin, Peter
2010
Designing the dynamics of globally coupled oscillators. Zbl 1196.34046
Orosz, Gábor; Moehlis, Jeff; Ashwin, Peter
2009
On planar piecewise and two-torus parabolic maps. Zbl 1176.37017
Ashwin, Peter; Fu, Xinchu; Lin, Congping
2009
Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators. Zbl 1178.34041
Ashwin, Peter; Burylko, Oleksandr; Maistrenko, Yuri
2008
Packings induced by piecewise isometries cannot contain the Arbelos. Zbl 1156.52013
Trovati, Marcello; Ashwin, Peter; Byott, Nigel
2008
Dynamics on networks of cluster states for globally coupled phase oscillators. Zbl 1167.34326
Ashwin, Peter; Orosz, Gábor; Wordsworth, John; Townley, Stuart
2007
The $$1:\sqrt 2$$ mode interaction and heteroclinic networks in Boussinesq convection. Zbl 1141.76453
Podvigina, Olga; Ashwin, Peter
2007
Tangency properties of a pentagonal tiling generated by a piecewise isometry. Zbl 1163.37379
Trovati, Marcello; Ashwin, Peter
2007
Polygonal invariant curves for a planar piecewise isometry. Zbl 1080.37009
Ashwin, Peter; Goetz, Arek
2006
Modelling instability $$ABC$$ flow using a mode interaction between steady and Hopf bifurcations with rotational symmetries of the cube. Zbl 1091.35520
Podvigina, Olga; Ashwin, Peter; Hawker, David
2006
Unstable attractors: existence and robustness in networks of oscillators with delayed pulse coupling. Zbl 1084.37061
Ashwin, Peter; Timme, Marc
2005
Discrete computation using a perturbed heteroclinic network. Zbl 1195.34053
Ashwin, Peter; Borresen, Jon
2005
Invariant curves and explosion of periodic islands in systems of piecewise rotations. Zbl 1090.37029
Ashwin, Peter; Goetz, Arek
2005
Product dynamics for homoclinic attractors. Zbl 1145.37307
Ashwin, Peter; Field, Michael
2005
Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators. Zbl 1086.37041
Ashwin, P.; Dangelmayr, G.
2005
Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria. Zbl 1093.37509
Hawker, David; Ashwin, Peter
2005
Riddled basins and coupled dynamical systems. Zbl 1103.37019
Ashwin, P.
2005
Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory. Zbl 1051.37041
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob
2004
Cycling chaotic attractors in two models for dynamics with invariant subspaces. Zbl 1080.37026
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob
2004
Internal dynamics of intermittency. Zbl 1080.37036
Sturman, Rob; Ashwin, Peter
2004
Symbolic analysis for some planar piecewise linear maps. Zbl 1042.37009
Fu, Xin-Chu; Ashwin, Peter
2003
Hopf bifurcation with cubic symmetry and instability of ABC flow. Zbl 1116.37310
Ashwin, Peter; Podvigina, Olga
2003
Properties of the invariant disk packing in a model bandpass sigma-delta modulator. Zbl 1056.37059
Ashwin, Peter; Fu, Xin-Chu; Deane, Jonathan
2003
Phase resetting effects for robust cycles between chaotic sets. Zbl 1080.37518
Ashwin, Peter; Field, Michael; Rucklidge, Alastair M.; Sturman, Rob
2003
Convergence to local random attractors. Zbl 1136.37345
Ashwin, Peter; Ochs, Gunter
2003
Cycling attractors of coupled cell systems and dynamics with symmetry. Zbl 1050.37047
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob
2003
Patchwork patterns: Dynamics on unbounded domains. Zbl 1032.37013
Ashwin, Peter
2003
Travelling fronts for the KPP equation with spatio-temporal delay. Zbl 1005.92024
Ashwin, P.; Bartuccelli, M. V.; Bridges, T. J.; Gourley, S. A.
2002
On the geometry of orientation-preserving planar piecewise isometries. Zbl 1100.37027
Ashwin, P.; Fu, X.-C.
2002
Riddling and invariance for discontinuous maps preserving Lebesgue measure. Zbl 1073.37009
Ashwin, Peter; Fu, Xin-Chu; Terry, John R.
2002
On the dynamics of some nonhyperbolic area-preserving piecewise linear maps. Zbl 1013.37039
Ashwin, Peter; Fu, Xin-Chu
2002
Group theoretic conditions for existence of robust relative homoclinic trajectories. Zbl 1039.37015
Ashwin, Peter; Montaldi, James
2002
Tangencies in invariant disc packings for certain planar piecewise isometries are rare. Zbl 1032.37026
Ashwin, Peter; Fu, Xin-Chu
2001
Euclidean extensions of dynamical systems. Zbl 1183.37043
Nicol, Matthew; Melbourne, Ian; Ashwin, Peter
2001
Symbolic representations of iterated maps. Zbl 1021.37007
Fu, Xin-Chu; Lu, Weiping; Ashwin, Peter; Duan, Jinqiao
2001
Hypermeander of spirals: local bifurcations and statistical properties. Zbl 1049.92001
Ashwin, P.; Melbourne, I.; Nicol, M.
2001
On riddling and weak attractors. Zbl 0954.37015
Ashwin, Peter; Terry, John R.
2000
Invariant sets for discontinuous parabolic area-preserving torus maps. Zbl 0952.37007
Ashwin, Peter; Fu, Xin-Chu; Nishikawa, Takashi; Życzkowski, Karol
2000
Isochronicity-induced bifurcations in systems of weakly dissipative coupled oscillators. Zbl 0976.34033
Ashwin, Peter; Dangelmayr, Gerhard
2000
Drift for Euclidean extensions of dynamical systems. Zbl 0976.37011
Ashwin, Peter; Melbourne, Ian; Nicol, Matthew
2000
Heteroclinic networks in coupled cell systems. Zbl 0947.37012
Ashwin, Peter; Field, Michael
1999
Transverse instability for non-normal parameters. Zbl 0984.37053
Ashwin, Peter; Covas, Eurico; Tavakol, Reza
1999
Attractors of a randomly forced electronic oscillator. Zbl 1065.94567
Ashwin, Peter
1999
Drift bifurcations of relative equilibria and transitions of spiral waves. Zbl 0958.37017
Ashwin, Peter; Melbourne, Ian; Nicol, Matthew
1999
Minimal attractors and bifurcations of random dynamical systems. Zbl 0934.37049
Ashwin, Peter
1999
Chaotic intermittency of patterns in symmetric systems. Zbl 0999.37033
Ashwin, Peter
1999
Attractors for robust heteroclinic cycles with continua of connections. Zbl 0901.58045
Ashwin, P.; Chossat, P.
1998
On the unfolding of a blowout bifurcation. Zbl 0930.37013
Ashwin, Peter; Aston, Philip J.; Nicol, Matthew
1998
Cycling chaos: Its creation, persistence and loss of stability in a model of nonlinear magnetoconvection. Zbl 0955.76035
Ashwin, Peter; Rucklidge, A. M.
1998
Boundary of two frequency behaviour in a system of three weakly coupled electronic oscillators. Zbl 0956.37013
Ashwin, Peter
1998
Blowout bifurcations of codimension two. Zbl 1044.37515
Ashwin, Peter; Aston, Philip J.
1998
A numerical bifurcation function for homoclinic orbits. Zbl 0911.34046
Ashwin, Peter; Mei, Zhen
1998
Elliptic behaviour in the sawtooth standard map. Zbl 1053.37520
Ashwin, Peter
1997
Noncompact drift for relative equilibria and relative periodic orbits. Zbl 0912.35079
Ashwin, Peter; Melbourne, Ian
1997
Lossless digital filter overflow oscillations; approximation of invariant fractals. Zbl 0902.65100
Ashwin, Peter; Chambers, W.; Petkov, G.
1997
A study of particle paths in non-axisymmetric Taylor-Couette flows. Zbl 0889.76089
Ashwin, P.; King, G. P.
1997
Detection of symmetry of attractors from observations. I: Theory. Zbl 0894.58037
Ashwin, Peter; Nicol, Matthew
1997
Cycles homoclinic to chaotic sets; robustness and resonance. Zbl 1012.37020
Ashwin, Peter
1997
Detection of symmetry of attractors from observations. II: An experiment with S$$_4$$ symmetry. Zbl 0894.58038
Ashwin, Peter; Tomes, Jörg
1997
From attractor to chaotic saddle: A tale of transverse instability. Zbl 0887.58034
Ashwin, Peter; Buescu, Jorge; Stewart, Ian
1996
Semirotors in the Josephson junction equations. Zbl 0843.34041
Aronson, D. G.; Krupa, M.; Ashwin, P.
1996
Forced symmetry breaking of homoclinic cycles in a PDE with O(2) symmetry. Zbl 0858.65123
Ashwin, Peter; Böhmer, Klaus; Mei, Z.
1996
Torus doubling in four weakly coupled oscillators. Zbl 0885.58056
Ashwin, Peter; Swift, James W.
1995
Normal form for Hopf bifurcation of partial differential equations on the square. Zbl 0839.35010
Ashwin, Peter; Mei, Z.
1995
A numerical Liapunov-Schmidt method with applications to Hopf bifurcation on a square. Zbl 0829.65075
Ashwin, Peter; Böhmer, Klaus; Mei, Zhen
1995
Streamline topology in eccentric Taylor vortex flow. Zbl 0882.76097
Ashwin, P.; King, G. P.
1995
Bifurcations of stationary, standing and travelling waves in triply diffusive convection. Zbl 0899.76165
Ashwin, Peter; Moroz, Irene; Roberts, Mark
1995
...and 15 more Documents
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#### Cited by 1,068 Authors

 58 Ashwin, Peter 19 Fu, Xinchu 12 Aguiar, Manuela A. D. 12 Dias, Ana Paula S. 11 Podvigina, Ol’ga Mikhaĭlovna 11 Stewart, Ian Nicholas 9 Bick, Christian 9 Castro, Sofia B. S. D. 9 Laing, Carlo R. 9 Li, Wan-Tong 9 Lohse, Alexander 9 Melbourne, Ian 9 Nicol, Matthew 9 Trofimchuk, Sergei I. 9 Wang, Zhi Cheng 8 Aston, Philip J. 8 Chen, Tianping 8 Field, Michael J. 7 Dangelmayr, Gerhard 7 Labouriau, Isabel S. 7 Lamb, Jeroen S. W. 7 Yu, Rongzhong 6 Bischi, Gian-Italo 6 Coombes, Stephen 6 Lu, Wenlian 6 Lueptow, Richard M. 6 Maistrenko, Yuri L. 6 Moehlis, Jeff 6 Ruan, Shigui 6 Rucklidge, Alastair M. 6 Timme, Marc 5 Bressloff, Paul C. 5 Burylko, Oleksandr 5 Chossat, Pascal 5 Du, Zengji 5 Goetz, Arek 5 Golubitsky, Martin A. 5 Grebogi, Celso 5 Ha, Seung-Yeal 5 Knobloch, Edgar 5 Omel’chenko, Oleh E. 5 Ott, Edward 5 Pecora, Louis M. 5 Pikovsky, Arkady S. 5 Postlethwaite, Claire M. 5 Rodrigues, Alexandre A. P. 5 Swift, James W. 4 Aihara, Kazuyuki 4 Blyuss, Konstantin B. 4 Buono, Pietro-Luciano 4 Carroll, Thomas L. 4 Collins, James J. 4 Gardini, Laura 4 Gottwald, Georg A. 4 Hasík, Karel 4 Huguet, Gemma 4 Inaba, Naohiko 4 Johnson, Gregg A. 4 Kamiyama, Kyohei 4 Kapitaniak, Tomasz 4 MacLaurin, James N. 4 Mei, Zhen 4 Rodrigues, Ana 4 Sturman, Rob 4 Viana, Ricardo Luiz 4 Wechselberger, Martin 4 Wulff, Claudia 4 Yanchuk, Sergiĭ Volodymyrovych 4 Yuan, Liguo 3 Afraimovich, Valentin S. 3 Aminzare, Zahra 3 Belhaq, Mohamed 3 Belykh, Igor V. 3 Belykh, Vladimir N. 3 Bloch, Anthony M. 3 Böhmer, Klaus 3 Borisyuk, Roman M. 3 Bruin, Henk 3 Cánovas, Jose S. 3 Chawanya, Tsuyoshi 3 Chen, Zhanhe 3 Chien, Cheng-Sheng 3 Crauel, Hans 3 Deane, Jonathan H. B. 3 Dellnitz, Michael 3 Duan, Jinqiao 3 Dudkowski, Dawid 3 Endo, Tetsuro 3 Fahsi, Abdelhak 3 Feng, Zhaosheng 3 Homburg, Ale Jan 3 Kahng, Byungik 3 Kim, Yongduck 3 Kirk, Vivien 3 Krawiecki, A. 3 Krupa, Martin 3 Kurths, Jürgen 3 Lai, Yingcheng 3 Li, Kun 3 Li, Zhuchun ...and 968 more Authors
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#### Cited in 128 Serials

 104 Chaos 85 Physica D 60 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 39 Dynamical Systems 27 Journal of Nonlinear Science 27 SIAM Journal on Applied Dynamical Systems 26 Chaos, Solitons and Fractals 18 Journal of Differential Equations 16 Nonlinearity 15 Communications in Nonlinear Science and Numerical Simulation 12 The Journal of Mathematical Neuroscience 9 Ergodic Theory and Dynamical Systems 8 Physics Letters. A 8 Journal of Dynamics and Differential Equations 8 Nonlinear Dynamics 7 Journal of Mathematical Biology 7 Dynamics and Stability of Systems 6 Journal of Mathematical Analysis and Applications 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Biological Cybernetics 5 Computer Methods in Applied Mechanics and Engineering 5 Journal of Statistical Physics 5 Applied Mathematics and Computation 5 Transactions of the American Mathematical Society 5 Physics of Fluids 5 Journal of Difference Equations and Applications 5 Communications on Pure and Applied Analysis 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Journal of Computational and Applied Mathematics 4 Proceedings of the American Mathematical Society 4 Nonlinear Analysis. Real World Applications 4 Journal of Theoretical Biology 3 Israel Journal of Mathematics 3 Mathematics and Computers in Simulation 3 Theoretical Population Biology 3 European Journal of Applied Mathematics 3 Neural Computation 3 Applied Mathematical Modelling 3 Journal of Mathematical Sciences (New York) 3 Abstract and Applied Analysis 3 Journal of Shanghai University 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Regular and Chaotic Dynamics 3 Journal of Dynamical and Control Systems 3 Discrete and Continuous Dynamical Systems. Series B 2 International Journal of Modern Physics B 2 Computers & Mathematics with Applications 2 Journal of Fluid Mechanics 2 Mathematical Methods in the Applied Sciences 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Journal of Geometry and Physics 2 Kybernetika 2 Mathematical and Computer Modelling 2 Japan Journal of Industrial and Applied Mathematics 2 Proceedings of the National Academy of Sciences of the United States of America 2 SIAM Review 2 Journal of Computational Neuroscience 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Qualitative Theory of Dynamical Systems 2 Stochastics and Dynamics 2 Discrete and Continuous Dynamical Systems. Series S 1 Modern Physics Letters B 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 International Journal of Systems Science 1 Journal of Computational Physics 1 Journal of Mathematical Physics 1 Mathematical Biosciences 1 Physica A 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Bulletin of Mathematical Biology 1 Theoretical and Computational Fluid Dynamics 1 Advances in Mathematics 1 Automatica 1 Computing 1 International Journal of Circuit Theory and Applications 1 International Journal of Game Theory 1 Inventiones Mathematicae 1 Journal of Approximation Theory 1 Journal of Functional Analysis 1 Journal of the London Mathematical Society. Second Series 1 Meccanica 1 Chinese Annals of Mathematics. Series B 1 Bulletin of the Iranian Mathematical Society 1 Boletim da Sociedade Portuguesa de Matemática 1 Journal of Symbolic Computation 1 Applied Mathematics Letters 1 Science in China. Series A 1 Neural Networks 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 International Journal of Computer Mathematics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Stochastic Processes and their Applications 1 Bulletin of the American Mathematical Society. New Series 1 Indagationes Mathematicae. New Series 1 Cybernetics and Systems Analysis 1 Experimental Mathematics ...and 28 more Serials
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#### Cited in 40 Fields

 379 Dynamical systems and ergodic theory (37-XX) 290 Ordinary differential equations (34-XX) 176 Biology and other natural sciences (92-XX) 108 Partial differential equations (35-XX) 32 Fluid mechanics (76-XX) 31 Numerical analysis (65-XX) 26 Mechanics of particles and systems (70-XX) 24 Systems theory; control (93-XX) 23 Information and communication theory, circuits (94-XX) 22 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 20 Combinatorics (05-XX) 16 Difference and functional equations (39-XX) 16 Probability theory and stochastic processes (60-XX) 15 Global analysis, analysis on manifolds (58-XX) 15 Computer science (68-XX) 15 Statistical mechanics, structure of matter (82-XX) 8 Geophysics (86-XX) 8 Operations research, mathematical programming (90-XX) 6 Mechanics of deformable solids (74-XX) 5 Measure and integration (28-XX) 5 Operator theory (47-XX) 5 Convex and discrete geometry (52-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Group theory and generalizations (20-XX) 3 Integral equations (45-XX) 3 Statistics (62-XX) 3 Optics, electromagnetic theory (78-XX) 3 Astronomy and astrophysics (85-XX) 2 General and overarching topics; collections (00-XX) 2 Number theory (11-XX) 2 Commutative algebra (13-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX)