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Author ID: ashwin.peter Recent zbMATH articles by "Ashwin, Peter"
Published as: Ashwin, Peter; Ashwin, P.
External Links: ORCID
all top 5

Co-Authors

11 single-authored
9 Fu, Xinchu
7 Mei, Zhen
7 Nicol, Matthew
7 Sturman, Rob
6 Bick, Christian
6 Creaser, Jennifer L.
6 Melbourne, Ian
6 Postlethwaite, Claire M.
6 Rodrigues, Ana
6 Tsaneva-Atanasova, Krasimira T.
5 Podvigina, Ol’ga Mikhaĭlovna
5 Rucklidge, Alastair M.
5 Stewart, Ian Nicholas
5 Swift, James W.
5 Wieczorek, Sebastian M.
4 Böhmer, Klaus
4 Field, Michael J.
4 Goetz, Arek
4 Karabacak, Özkan
4 King, Gregory P.
3 Alkhayuon, Hassan M.
3 Burylko, Oleksandr
3 Chossat, Pascal
3 Cox, Peter M.
3 Dangelmayr, Gerhard
3 Hawker, David
3 Lin, Congping
3 Orosz, Gábor
3 Terry, John R.
2 Aston, Philip J.
2 Borresen, Jon
2 Buescu, Jorge
2 Ceni, Andrea
2 Cockram, Noah
2 Luke, C. M.
2 Poignard, Camille
2 Smug, Damian
2 Sornette, Didier
2 Trovati, Marcello
1 Aguiar, Manuela A. D.
1 Allgower, Eugene L.
1 Aronson, Donald G.
1 Ashwin, Julian
1 Azad, Abul Kalam Al
1 Bartuccelli, Michele V.
1 Bassom, Andrew P.
1 Benjamin, Oscar
1 Blyuss, Konstantin B.
1 Boers, Niklas
1 Breakspear, Michael
1 Britz, Juliane
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 Ditlevsen, Peter D.
1 Duan, Jinqiao
1 Fitzgerald, Thomas H. B.
1 Glendinning, Paul Alexander
1 Gourley, Stephen A.
1 Guaschi, John
1 Huguet, Gemma
1 Hummel, Felix
1 Ikegami, Gikō
1 Ismail, Asma
1 Jackson, Laura C.
1 Krupa, Martin
1 Kühn, Christian
1 Lavric, Aureliu
1 Livi, Lorenzo
1 Lohse, Alexander
1 Lu, Weiping
1 Maistrenko, Yuri L.
1 Moehlis, Jeff
1 Montaldi, James
1 Moroz, Irene M.
1 Morr, Andreas
1 Newman, Julian
1 Nicks, Rachel
1 Nijhof, J. H. B.
1 Nishikawa, Takashi
1 Nowotny, Thomas
1 Nyman, Karl H. M.
1 Ochs, Gunter
1 Peres, Pedro L. D.
1 Pérez-Cervera, Alberto
1 Perryman, Clare
1 Petkov, Georgi P.
1 Phelps, J. M.
1 Quinn, Courtney
1 Rankin, James
1 Richardson, Mark P.
1 Roberts, Richard Mark
...and 19 more Co-Authors
all top 5

Serials

19 Physica D
17 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
5 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 Biological Cybernetics
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 Communications in Nonlinear Science and Numerical Simulation
1 Quantitative Finance
1 Discrete and Continuous Dynamical Systems. Series B
1 Progress of Theoretical Physics
1 Stochastics and Dynamics
1 Journal of Theoretical Biology
1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences

Publications by Year

Citations contained in zbMATH Open

125 Publications have been cited 1,620 times in 950 Documents Cited by Year
From attractor to chaotic saddle: A tale of transverse instability. Zbl 0887.58034
Ashwin, Peter; Buescu, Jorge; Stewart, Ian
127
1996
Bubbling of attractors and synchronisation of chaotic oscillators. Zbl 0959.37508
Ashwin, Peter; Buescu, Jorge; Stewart, Ian
99
1994
The dynamics of \(n\) weakly coupled identical oscillators. Zbl 0872.58049
Ashwin, P.; Swift, J. W.
95
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.
83
2002
Mathematical frameworks for oscillatory network dynamics in neuroscience. Zbl 1356.92015
Ashwin, Peter; Coombes, Stephen; Nicks, Rachel
73
2016
Weak chimeras in minimal networks of coupled phase oscillators. Zbl 1345.34052
Ashwin, Peter; Burylko, Oleksandr
43
2015
Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation. Zbl 1254.37053
Aguiar, M.; Ashwin, P.; Dias, A.; Field, M.
40
2011
Three identical oscillators with symmetric coupling. Zbl 0708.58020
Ashwin, Peter; King, G. P.; Swift, James W.
34
1990
Heteroclinic networks in coupled cell systems. Zbl 0947.37012
Ashwin, Peter; Field, Michael
33
1999
On designing heteroclinic networks from graphs. Zbl 1417.37098
Ashwin, Peter; Postlethwaite, Claire
31
2013
Hopf normal form with \(S_N\) symmetry and reduction to systems of nonlinearly coupled phase oscillators. Zbl 1364.34041
Ashwin, Peter; Rodrigues, Ana
30
2016
Dynamics on networks of cluster states for globally coupled phase oscillators. Zbl 1167.34326
Ashwin, Peter; Orosz, Gábor; Wordsworth, John; Townley, Stuart
30
2007
On local attraction properties and a stability index for heteroclinic connections. Zbl 1219.37021
Podvigina, Olga; Ashwin, Peter
30
2011
Parameter shifts for nonautonomous systems in low dimension: bifurcation- and rate-induced tipping. Zbl 1435.37104
Ashwin, Peter; Perryman, Clare; Wieczorek, Sebastian
27
2017
Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators. Zbl 1178.34041
Ashwin, Peter; Burylko, Oleksandr; Maistrenko, Yuri
26
2008
Chaotic weak chimeras and their persistence in coupled populations of phase oscillators. Zbl 1355.37041
Bick, Christian; Ashwin, Peter
24
2016
Elliptic behaviour in the sawtooth standard map. Zbl 1053.37520
Ashwin, Peter
24
1997
Noncompact drift for relative equilibria and relative periodic orbits. Zbl 0912.35079
Ashwin, Peter; Melbourne, Ian
24
1997
Chaos in generically coupled phase oscillator networks with nonpairwise interactions. Zbl 1382.34038
Bick, Christian; Ashwin, Peter; Rodrigues, Ana
24
2016
Excitability in ramped systems: the compost-bomb instability. Zbl 1219.86006
Wieczorek, S.; Ashwin, P.; Luke, C. M.; Cox, P. M.
23
2011
On the geometry of orientation-preserving planar piecewise isometries. Zbl 1100.37027
Ashwin, P.; Fu, X.-C.
22
2002
Lossless digital filter overflow oscillations; approximation of invariant fractals. Zbl 0902.65100
Ashwin, Peter; Chambers, W.; Petkov, G.
22
1997
Attractors for robust heteroclinic cycles with continua of connections. Zbl 0901.58045
Ashwin, P.; Chossat, P.
21
1998
On the unfolding of a blowout bifurcation. Zbl 0930.37013
Ashwin, Peter; Aston, Philip J.; Nicol, Matthew
20
1998
Transverse instability for non-normal parameters. Zbl 0984.37053
Ashwin, Peter; Covas, Eurico; Tavakol, Reza
20
1999
Rate-induced tipping from periodic attractors: partial tipping and connecting orbits. Zbl 1392.37026
Alkhayuon, Hassan M.; Ashwin, Peter
18
2018
Unstable attractors: existence and robustness in networks of oscillators with delayed pulse coupling. Zbl 1084.37061
Ashwin, Peter; Timme, Marc
18
2005
On riddling and weak attractors. Zbl 0954.37015
Ashwin, Peter; Terry, John R.
17
2000
Tangencies in invariant disc packings for certain planar piecewise isometries are rare. Zbl 1032.37026
Ashwin, Peter; Fu, Xin-Chu
16
2001
Hopf bifurcation with cubic symmetry and instability of ABC flow. Zbl 1116.37310
Ashwin, Peter; Podvigina, Olga
15
2003
Symbolic representations of iterated maps. Zbl 1021.37007
Fu, Xin-Chu; Lu, Weiping; Ashwin, Peter; Duan, Jinqiao
14
2001
Riddling and invariance for discontinuous maps preserving Lebesgue measure. Zbl 1073.37009
Ashwin, Peter; Fu, Xin-Chu; Terry, John R.
14
2002
Criteria for robustness of heteroclinic cycles in neural microcircuits. Zbl 1259.37054
Ashwin, Peter; Karabacak, Özkan; Nowotny, Thomas
14
2011
Symbolic analysis for some planar piecewise linear maps. Zbl 1042.37009
Fu, Xin-Chu; Ashwin, Peter
14
2003
Discrete computation using a perturbed heteroclinic network. Zbl 1195.34053
Ashwin, Peter; Borresen, Jon
14
2005
Polygonal invariant curves for a planar piecewise isometry. Zbl 1080.37009
Ashwin, Peter; Goetz, Arek
13
2006
Euclidean extensions of dynamical systems. Zbl 1183.37043
Nicol, Matthew; Melbourne, Ian; Ashwin, Peter
13
2001
Invariant curves and explosion of periodic islands in systems of piecewise rotations. Zbl 1090.37029
Ashwin, Peter; Goetz, Arek
13
2005
Designing the dynamics of globally coupled oscillators. Zbl 1196.34046
Orosz, Gábor; Moehlis, Jeff; Ashwin, Peter
12
2009
Symmetry groups of attractors. Zbl 0817.58020
Ashwin, Peter; Melbourne, Ian
11
1994
A Hopf bifurcation with Robin boundary conditions. Zbl 0807.35013
Ashwin, Peter; Mei, Zhen
11
1994
Symmetric chaos in systems of three and four forced oscillators. Zbl 0711.94031
Ashwin, Peter
11
1990
Almost complete and equable heteroclinic networks. Zbl 1431.34058
Ashwin, Peter; Castro, Sofia B. S. D.; Lohse, Alexander
11
2020
Basin bifurcations, oscillatory instability and rate-induced thresholds for Atlantic meridional overturning circulation in a global oceanic box model. Zbl 1472.86003
Alkhayuon, Hassan; Ashwin, Peter; Jackson, Laura C.; Quinn, Courtney; Wood, Richard A.
11
2019
Properties of the invariant disk packing in a model bandpass sigma-delta modulator. Zbl 1056.37059
Ashwin, Peter; Fu, Xin-Chu; Deane, Jonathan
10
2003
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.
10
2012
Designing heteroclinic and excitable networks in phase space using two populations of coupled cells. Zbl 1362.37058
Ashwin, Peter; Postlethwaite, Claire
10
2016
A study of particle paths in non-axisymmetric Taylor-Couette flows. Zbl 0889.76089
Ashwin, P.; King, G. P.
9
1997
Normal form for Hopf bifurcation of partial differential equations on the square. Zbl 0839.35010
Ashwin, Peter; Mei, Z.
9
1995
Heteroclinic ratchets in networks of coupled oscillators. Zbl 1208.34057
Karabacak, Özkan; Ashwin, Peter
9
2010
Cycling chaos: Its creation, persistence and loss of stability in a model of nonlinear magnetoconvection. Zbl 0955.76035
Ashwin, Peter; Rucklidge, A. M.
8
1998
Rotation sets and phase-locking in an electronic three oscillator system. Zbl 0784.34027
Ashwin, Peter; Guaschi, John; Phelps, J. M.
7
1993
Torus doubling in four weakly coupled oscillators. Zbl 0885.58056
Ashwin, Peter; Swift, James W.
7
1995
On the dynamics of some nonhyperbolic area-preserving piecewise linear maps. Zbl 1013.37039
Ashwin, Peter; Fu, Xin-Chu
7
2002
Local and global stability indices for a riddled basin attractor of a piecewise linear map. Zbl 1370.37057
Roslan, Ummu Atiqah Mohd; Ashwin, Peter
7
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
7
2004
Within-burst synchrony changes for coupled elliptic bursters. Zbl 1195.37032
Azad, Abul Kalam Al; Ashwin, Peter
7
2010
The \(1:\sqrt 2\) mode interaction and heteroclinic networks in Boussinesq convection. Zbl 1141.76453
Podvigina, Olga; Ashwin, Peter
7
2007
A numerical Liapunov-Schmidt method with applications to Hopf bifurcation on a square. Zbl 0829.65075
Ashwin, Peter; Böhmer, Klaus; Mei, Zhen
6
1995
Boundary of two frequency behaviour in a system of three weakly coupled electronic oscillators. Zbl 0956.37013
Ashwin, Peter
6
1998
Invariant sets for discontinuous parabolic area-preserving torus maps. Zbl 0952.37007
Ashwin, Peter; Fu, Xin-Chu; Nishikawa, Takashi; Życzkowski, Karol
6
2000
Quantifying noisy attractors: from heteroclinic to excitable networks. Zbl 1360.37141
Ashwin, Peter; Postlethwaite, Claire
6
2016
Drift bifurcations of relative equilibria and transitions of spiral waves. Zbl 0958.37017
Ashwin, Peter; Melbourne, Ian; Nicol, Matthew
6
1999
Attractors of a randomly forced electronic oscillator. Zbl 1065.94567
Ashwin, Peter
6
1999
Phase resetting effects for robust cycles between chaotic sets. Zbl 1080.37518
Ashwin, Peter; Field, Michael; Rucklidge, Alastair M.; Sturman, Rob
6
2003
Sequential noise-induced escapes for oscillatory network dynamics. Zbl 1387.60088
Creaser, Jennifer; Tsaneva-Atanasova, Krasimira; Ashwin, Peter
6
2018
Minimal attractors and bifurcations of random dynamical systems. Zbl 0934.37049
Ashwin, Peter
5
1999
Streamline topology in eccentric Taylor vortex flow. Zbl 0882.76097
Ashwin, P.; King, G. P.
5
1995
Detection of symmetry of attractors from observations. I: Theory. Zbl 0894.58037
Ashwin, Peter; Nicol, Matthew
5
1997
High corank steady-state mode interactions on a rectangle. Zbl 0769.35006
Ashwin, Peter
5
1992
Hypermeander of spirals: local bifurcations and statistical properties. Zbl 1049.92001
Ashwin, P.; Melbourne, I.; Nicol, M.
5
2001
Cycles homoclinic to chaotic sets; robustness and resonance. Zbl 1012.37020
Ashwin, Peter
5
1997
Tangency properties of a pentagonal tiling generated by a piecewise isometry. Zbl 1163.37379
Trovati, Marcello; Ashwin, Peter
5
2007
Convergence to local random attractors. Zbl 1136.37345
Ashwin, Peter; Ochs, Gunter
5
2003
From coupled networks of systems to networks of states in phase space. Zbl 1395.37061
Weinberger, Oskar; Ashwin, Peter
5
2018
A low-dimensional model of binocular rivalry using winnerless competition. Zbl 1194.91167
Ashwin, Peter; Lavric, Aureliu
5
2010
Product dynamics for homoclinic attractors. Zbl 1145.37307
Ashwin, Peter; Field, Michael
5
2005
A numerical Liapunov-Schmidt method for finitely determined problems. Zbl 0787.58044
Ashwin, P.; Böhmer, K.; Mei, Z.
4
1993
Permissible symmetries of coupled cell networks. Zbl 0816.58035
Ashwin, Peter; Stork, Peter
4
1994
Forced symmetry breaking of homoclinic cycles in a PDE with O(2) symmetry. Zbl 0858.65123
Ashwin, Peter; Böhmer, Klaus; Mei, Z.
4
1996
Semirotors in the Josephson junction equations. Zbl 0843.34041
Aronson, D. G.; Krupa, M.; Ashwin, P.
4
1996
Extreme sensitivity and climate tipping points. Zbl 1446.37075
Ashwin, Peter; von der Heydt, Anna S.
4
2020
State-dependent effective interactions in oscillator networks through coupling functions with dead zones. Zbl 1462.34058
Ashwin, Peter; Bick, Christian; Poignard, Camille
4
2019
Rate-induced tipping: thresholds, edge states and connecting orbits. Zbl 1521.34050
Wieczorek, Sebastian; Xie, Chun; Ashwin, Peter
4
2023
Robust heteroclinic behaviour, synchronization, and ratcheting of coupled oscillators. Zbl 1266.34059
Ashwin, Peter; Karabacak, Özkan
4
2011
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
4
2006
On statistical attractors and the convergence of time averages. Zbl 1214.37024
Karabacak, Özkan; Ashwin, Peter
4
2011
Heteroclinic switching in coupled oscillator networks: dynamics on odd graphs. Zbl 1221.37044
Ashwin, Peter; Orosz, Gábor; Borresen, Jon
4
2010
Unfolding the torus: Oscillator geometry from time delays. Zbl 0804.34036
Ashwin, P.; Swift, J. W.
3
1993
Bifurcations of stationary, standing and travelling waves in triply diffusive convection. Zbl 0899.76165
Ashwin, Peter; Moroz, Irene; Roberts, Mark
3
1995
Measuring rotation sets of coupled oscillators. Zbl 0809.34051
Ashwin, Peter; Swift, James W.
3
1994
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
3
2019
The echo index and multistability in input-driven recurrent neural networks. Zbl 1484.68181
Ceni, Andrea; Ashwin, Peter; Livi, Lorenzo; Postlethwaite, Claire
3
2020
Existence and stability of Chimera states in a minimal system of phase oscillators. Zbl 1400.34059
Thoubaan, Mary; Ashwin, Peter
3
2018
Blowout bifurcations of codimension two. Zbl 1044.37515
Ashwin, Peter; Aston, Philip J.
3
1998
Isochronicity-induced bifurcations in systems of weakly dissipative coupled oscillators. Zbl 0976.34033
Ashwin, Peter; Dangelmayr, Gerhard
3
2000
Noise-induced switching near a depth two heteroclinic network and an application to Boussinesq convection. Zbl 1311.37013
Ashwin, Peter; Podvigina, Olga
3
2010
Cycling chaotic attractors in two models for dynamics with invariant subspaces. Zbl 1080.37026
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob
3
2004
Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators. Zbl 1086.37041
Ashwin, P.; Dangelmayr, G.
3
2005
On planar piecewise and two-torus parabolic maps. Zbl 1176.37017
Ashwin, Peter; Fu, Xinchu; Lin, Congping
3
2009
Rate-induced tipping: thresholds, edge states and connecting orbits. Zbl 1521.34050
Wieczorek, Sebastian; Xie, Chun; Ashwin, Peter
4
2023
Physical measures of asymptotically autonomous dynamical systems. Zbl 1523.37028
Newman, Julian; Ashwin, Peter
1
2023
Reduction methods in climate dynamics – a brief review. Zbl 1509.86001
Hummel, Felix; Ashwin, Peter; Kuehn, Christian
1
2023
From symmetric networks to heteroclinic dynamics and chaos in coupled phase oscillators with higher-order interactions. Zbl 1509.37053
Ashwin, Peter; Bick, Christian; Rodrigues, Ana
1
2022
Noisy network attractor models for transitions between EEG microstates. Zbl 1467.92105
Creaser, Jennifer; Ashwin, Peter; Postlethwaite, Claire; Britz, Juliane
1
2021
Almost complete and equable heteroclinic networks. Zbl 1431.34058
Ashwin, Peter; Castro, Sofia B. S. D.; Lohse, Alexander
11
2020
Extreme sensitivity and climate tipping points. Zbl 1446.37075
Ashwin, Peter; von der Heydt, Anna S.
4
2020
The echo index and multistability in input-driven recurrent neural networks. Zbl 1484.68181
Ceni, Andrea; Ashwin, Peter; Livi, Lorenzo; Postlethwaite, Claire
3
2020
Bifurcation of critical sets and relaxation oscillations in singular fast-slow systems. Zbl 07459749
Nyman, Karl H. M.; Ashwin, Peter; Ditlevsen, Peter D.
3
2020
Basin bifurcations, oscillatory instability and rate-induced thresholds for Atlantic meridional overturning circulation in a global oceanic box model. Zbl 1472.86003
Alkhayuon, Hassan; Ashwin, Peter; Jackson, Laura C.; Quinn, Courtney; Wood, Richard A.
11
2019
State-dependent effective interactions in oscillator networks through coupling functions with dead zones. Zbl 1462.34058
Ashwin, Peter; Bick, Christian; Poignard, Camille
4
2019
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
3
2019
Rate-induced tipping from periodic attractors: partial tipping and connecting orbits. Zbl 1392.37026
Alkhayuon, Hassan M.; Ashwin, Peter
18
2018
Sequential noise-induced escapes for oscillatory network dynamics. Zbl 1387.60088
Creaser, Jennifer; Tsaneva-Atanasova, Krasimira; Ashwin, Peter
6
2018
From coupled networks of systems to networks of states in phase space. Zbl 1395.37061
Weinberger, Oskar; Ashwin, Peter
5
2018
Existence and stability of Chimera states in a minimal system of phase oscillators. Zbl 1400.34059
Thoubaan, Mary; Ashwin, Peter
3
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
2
2018
Parameter shifts for nonautonomous systems in low dimension: bifurcation- and rate-induced tipping. Zbl 1435.37104
Ashwin, Peter; Perryman, Clare; Wieczorek, Sebastian
27
2017
Mathematical frameworks for oscillatory network dynamics in neuroscience. Zbl 1356.92015
Ashwin, Peter; Coombes, Stephen; Nicks, Rachel
73
2016
Hopf normal form with \(S_N\) symmetry and reduction to systems of nonlinearly coupled phase oscillators. Zbl 1364.34041
Ashwin, Peter; Rodrigues, Ana
30
2016
Chaotic weak chimeras and their persistence in coupled populations of phase oscillators. Zbl 1355.37041
Bick, Christian; Ashwin, Peter
24
2016
Chaos in generically coupled phase oscillator networks with nonpairwise interactions. Zbl 1382.34038
Bick, Christian; Ashwin, Peter; Rodrigues, Ana
24
2016
Designing heteroclinic and excitable networks in phase space using two populations of coupled cells. Zbl 1362.37058
Ashwin, Peter; Postlethwaite, Claire
10
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
7
2016
Quantifying noisy attractors: from heteroclinic to excitable networks. Zbl 1360.37141
Ashwin, Peter; Postlethwaite, Claire
6
2016
Weak chimeras in minimal networks of coupled phase oscillators. Zbl 1345.34052
Ashwin, Peter; Burylko, Oleksandr
43
2015
Multi-cluster dynamics in coupled phase oscillator networks. Zbl 1351.37206
Ismail, Asma; Ashwin, Peter
1
2015
On designing heteroclinic networks from graphs. Zbl 1417.37098
Ashwin, Peter; Postlethwaite, Claire
31
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.
10
2012
Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation. Zbl 1254.37053
Aguiar, M.; Ashwin, P.; Dias, A.; Field, M.
40
2011
On local attraction properties and a stability index for heteroclinic connections. Zbl 1219.37021
Podvigina, Olga; Ashwin, Peter
30
2011
Excitability in ramped systems: the compost-bomb instability. Zbl 1219.86006
Wieczorek, S.; Ashwin, P.; Luke, C. M.; Cox, P. M.
23
2011
Criteria for robustness of heteroclinic cycles in neural microcircuits. Zbl 1259.37054
Ashwin, Peter; Karabacak, Özkan; Nowotny, Thomas
14
2011
Robust heteroclinic behaviour, synchronization, and ratcheting of coupled oscillators. Zbl 1266.34059
Ashwin, Peter; Karabacak, Özkan
4
2011
On statistical attractors and the convergence of time averages. Zbl 1214.37024
Karabacak, Özkan; Ashwin, Peter
4
2011
Correction to: “Excitability in ramped systems: the compost-bomb instability”. Zbl 1221.86005
Wieczorek, S.; Ashwin, P.; Luke, C. M.; Cox, P. M.
2
2011
Heteroclinic ratchets in networks of coupled oscillators. Zbl 1208.34057
Karabacak, Özkan; Ashwin, Peter
9
2010
Within-burst synchrony changes for coupled elliptic bursters. Zbl 1195.37032
Azad, Abul Kalam Al; Ashwin, Peter
7
2010
A low-dimensional model of binocular rivalry using winnerless competition. Zbl 1194.91167
Ashwin, Peter; Lavric, Aureliu
5
2010
Heteroclinic switching in coupled oscillator networks: dynamics on odd graphs. Zbl 1221.37044
Ashwin, Peter; Orosz, Gábor; Borresen, Jon
4
2010
Noise-induced switching near a depth two heteroclinic network and an application to Boussinesq convection. Zbl 1311.37013
Ashwin, Peter; Podvigina, Olga
3
2010
Cone exchange transformations and boundedness of orbits. Zbl 1213.37063
Ashwin, Peter; Goetz, Arek
2
2010
A minimal system with a depth-two heteroclinic network. Zbl 1204.37027
Chawanya, Tsuyoshi; Ashwin, Peter
2
2010
Designing the dynamics of globally coupled oscillators. Zbl 1196.34046
Orosz, Gábor; Moehlis, Jeff; Ashwin, Peter
12
2009
On planar piecewise and two-torus parabolic maps. Zbl 1176.37017
Ashwin, Peter; Fu, Xinchu; Lin, Congping
3
2009
Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators. Zbl 1178.34041
Ashwin, Peter; Burylko, Oleksandr; Maistrenko, Yuri
26
2008
Packings induced by piecewise isometries cannot contain the Arbelos. Zbl 1156.52013
Trovati, Marcello; Ashwin, Peter; Byott, Nigel
2
2008
Dynamics on networks of cluster states for globally coupled phase oscillators. Zbl 1167.34326
Ashwin, Peter; Orosz, Gábor; Wordsworth, John; Townley, Stuart
30
2007
The \(1:\sqrt 2\) mode interaction and heteroclinic networks in Boussinesq convection. Zbl 1141.76453
Podvigina, Olga; Ashwin, Peter
7
2007
Tangency properties of a pentagonal tiling generated by a piecewise isometry. Zbl 1163.37379
Trovati, Marcello; Ashwin, Peter
5
2007
Polygonal invariant curves for a planar piecewise isometry. Zbl 1080.37009
Ashwin, Peter; Goetz, Arek
13
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
4
2006
Unstable attractors: existence and robustness in networks of oscillators with delayed pulse coupling. Zbl 1084.37061
Ashwin, Peter; Timme, Marc
18
2005
Discrete computation using a perturbed heteroclinic network. Zbl 1195.34053
Ashwin, Peter; Borresen, Jon
14
2005
Invariant curves and explosion of periodic islands in systems of piecewise rotations. Zbl 1090.37029
Ashwin, Peter; Goetz, Arek
13
2005
Product dynamics for homoclinic attractors. Zbl 1145.37307
Ashwin, Peter; Field, Michael
5
2005
Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators. Zbl 1086.37041
Ashwin, P.; Dangelmayr, G.
3
2005
Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria. Zbl 1093.37509
Hawker, David; Ashwin, Peter
2
2005
Riddled basins and coupled dynamical systems. Zbl 1103.37019
Ashwin, P.
1
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
7
2004
Cycling chaotic attractors in two models for dynamics with invariant subspaces. Zbl 1080.37026
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob
3
2004
Internal dynamics of intermittency. Zbl 1080.37036
Sturman, Rob; Ashwin, Peter
1
2004
Hopf bifurcation with cubic symmetry and instability of ABC flow. Zbl 1116.37310
Ashwin, Peter; Podvigina, Olga
15
2003
Symbolic analysis for some planar piecewise linear maps. Zbl 1042.37009
Fu, Xin-Chu; Ashwin, Peter
14
2003
Properties of the invariant disk packing in a model bandpass sigma-delta modulator. Zbl 1056.37059
Ashwin, Peter; Fu, Xin-Chu; Deane, Jonathan
10
2003
Phase resetting effects for robust cycles between chaotic sets. Zbl 1080.37518
Ashwin, Peter; Field, Michael; Rucklidge, Alastair M.; Sturman, Rob
6
2003
Convergence to local random attractors. Zbl 1136.37345
Ashwin, Peter; Ochs, Gunter
5
2003
Cycling attractors of coupled cell systems and dynamics with symmetry. Zbl 1050.37047
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob
2
2003
Patchwork patterns: Dynamics on unbounded domains. Zbl 1032.37013
Ashwin, Peter
1
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.
83
2002
On the geometry of orientation-preserving planar piecewise isometries. Zbl 1100.37027
Ashwin, P.; Fu, X.-C.
22
2002
Riddling and invariance for discontinuous maps preserving Lebesgue measure. Zbl 1073.37009
Ashwin, Peter; Fu, Xin-Chu; Terry, John R.
14
2002
On the dynamics of some nonhyperbolic area-preserving piecewise linear maps. Zbl 1013.37039
Ashwin, Peter; Fu, Xin-Chu
7
2002
Group theoretic conditions for existence of robust relative homoclinic trajectories. Zbl 1039.37015
Ashwin, Peter; Montaldi, James
2
2002
Tangencies in invariant disc packings for certain planar piecewise isometries are rare. Zbl 1032.37026
Ashwin, Peter; Fu, Xin-Chu
16
2001
Symbolic representations of iterated maps. Zbl 1021.37007
Fu, Xin-Chu; Lu, Weiping; Ashwin, Peter; Duan, Jinqiao
14
2001
Euclidean extensions of dynamical systems. Zbl 1183.37043
Nicol, Matthew; Melbourne, Ian; Ashwin, Peter
13
2001
Hypermeander of spirals: local bifurcations and statistical properties. Zbl 1049.92001
Ashwin, P.; Melbourne, I.; Nicol, M.
5
2001
On riddling and weak attractors. Zbl 0954.37015
Ashwin, Peter; Terry, John R.
17
2000
Invariant sets for discontinuous parabolic area-preserving torus maps. Zbl 0952.37007
Ashwin, Peter; Fu, Xin-Chu; Nishikawa, Takashi; Życzkowski, Karol
6
2000
Isochronicity-induced bifurcations in systems of weakly dissipative coupled oscillators. Zbl 0976.34033
Ashwin, Peter; Dangelmayr, Gerhard
3
2000
Drift for Euclidean extensions of dynamical systems. Zbl 0976.37011
Ashwin, Peter; Melbourne, Ian; Nicol, Matthew
1
2000
Heteroclinic networks in coupled cell systems. Zbl 0947.37012
Ashwin, Peter; Field, Michael
33
1999
Transverse instability for non-normal parameters. Zbl 0984.37053
Ashwin, Peter; Covas, Eurico; Tavakol, Reza
20
1999
Drift bifurcations of relative equilibria and transitions of spiral waves. Zbl 0958.37017
Ashwin, Peter; Melbourne, Ian; Nicol, Matthew
6
1999
Attractors of a randomly forced electronic oscillator. Zbl 1065.94567
Ashwin, Peter
6
1999
Minimal attractors and bifurcations of random dynamical systems. Zbl 0934.37049
Ashwin, Peter
5
1999
Chaotic intermittency of patterns in symmetric systems. Zbl 0999.37033
Ashwin, Peter
2
1999
Attractors for robust heteroclinic cycles with continua of connections. Zbl 0901.58045
Ashwin, P.; Chossat, P.
21
1998
On the unfolding of a blowout bifurcation. Zbl 0930.37013
Ashwin, Peter; Aston, Philip J.; Nicol, Matthew
20
1998
Cycling chaos: Its creation, persistence and loss of stability in a model of nonlinear magnetoconvection. Zbl 0955.76035
Ashwin, Peter; Rucklidge, A. M.
8
1998
Boundary of two frequency behaviour in a system of three weakly coupled electronic oscillators. Zbl 0956.37013
Ashwin, Peter
6
1998
Blowout bifurcations of codimension two. Zbl 1044.37515
Ashwin, Peter; Aston, Philip J.
3
1998
A numerical bifurcation function for homoclinic orbits. Zbl 0911.34046
Ashwin, Peter; Mei, Zhen
1
1998
Elliptic behaviour in the sawtooth standard map. Zbl 1053.37520
Ashwin, Peter
24
1997
Noncompact drift for relative equilibria and relative periodic orbits. Zbl 0912.35079
Ashwin, Peter; Melbourne, Ian
24
1997
Lossless digital filter overflow oscillations; approximation of invariant fractals. Zbl 0902.65100
Ashwin, Peter; Chambers, W.; Petkov, G.
22
1997
A study of particle paths in non-axisymmetric Taylor-Couette flows. Zbl 0889.76089
Ashwin, P.; King, G. P.
9
1997
Detection of symmetry of attractors from observations. I: Theory. Zbl 0894.58037
Ashwin, Peter; Nicol, Matthew
5
1997
Cycles homoclinic to chaotic sets; robustness and resonance. Zbl 1012.37020
Ashwin, Peter
5
1997
...and 25 more Documents
all top 5

Cited by 1,412 Authors

68 Ashwin, Peter
19 Fu, Xinchu
17 Aguiar, Manuela A. D.
17 Dias, Ana Paula S.
16 Bick, Christian
15 Podvigina, Ol’ga Mikhaĭlovna
12 Castro, Sofia B. S. D.
12 Maistrenko, Yuri L.
12 Stewart, Ian Nicholas
11 Lohse, Alexander
11 Postlethwaite, Claire M.
10 Trofimchuk, Sergei I.
9 Labouriau, Isabel S.
9 Laing, Carlo R.
9 Lamb, Jeroen S. W.
9 Li, Wan-Tong
9 Melbourne, Ian
9 Nicol, Matthew
9 Rodrigues, Alexandre A. P.
9 Wang, Zhi Cheng
8 Aston, Philip J.
8 Chen, Tianping
8 Kapitaniak, Tomasz
8 Kühn, Christian
8 Pikovsky, Arkady S.
8 Rucklidge, Alastair M.
7 Coombes, Stephen
7 Dangelmayr, Gerhard
7 Kurths, Jürgen
7 Moehlis, Jeff
7 Timme, Marc
7 Yanchuk, Sergiĭ Volodymyrovych
7 Yu, Rongzhong
6 Bischi, Gian-Italo
6 Bressloff, Paul C.
6 Burylko, Oleksandr
6 Du, Zengji
6 Field, Michael J.
6 Gardini, Laura
6 Goetz, Arek
6 Golubitsky, Martin A.
6 Grebogi, Celso
6 Lai, Yingcheng
6 Lu, Wenlian
6 Lueptow, Richard M.
6 Omel’chenko, Oleh E.
6 Osipov, Grigory V.
6 Ott, Edward
6 Ruan, Shigui
5 Blyuss, Konstantin B.
5 Chossat, Pascal
5 Ha, Seung-Yeal
5 Jones, Christopher K. R. T.
5 Knobloch, Edgar
5 Li, Kun
5 MacLaurin, James N.
5 Mei, Zhen
5 Palacios, Antonio
5 Pecora, Louis M.
5 Popovych, Oleksandr V.
5 Rodrigues, Ana
5 Sieber, Jan
5 Swift, James W.
5 Wieczorek, Sebastian M.
4 Afraimovich, Valentin S.
4 Aihara, Kazuyuki
4 Buono, Pietro-Luciano
4 Campbell, Sue Ann
4 Cánovas, Jose S.
4 Carroll, Thomas L.
4 Collins, James J.
4 Dellnitz, Michael
4 Feng, Zhaosheng
4 Garrido-da-Silva, Liliana
4 Gottwald, Georg A.
4 Grines, Evgeny A.
4 Hasík, Karel
4 Huguet, Gemma
4 In, Visarath
4 Inaba, Naohiko
4 Johnson, Gregg A.
4 Kahng, Byungik
4 Kamiyama, Kyohei
4 Kirk, Vivien
4 Krischer, Katharina
4 Kuznetsov, Aleksandr Petrovich
4 Martens, Erik Andreas
4 Mosekilde, Erik
4 Nakao, Hiroya
4 Sherratt, Jonathan A.
4 Strogatz, Steven Henry
4 Sturman, Rob
4 Turukina, Ludmila V.
4 Viana, Ricardo Luiz
4 Wechselberger, Martin
4 Wulff, Claudia
4 Yuan, Liguo
4 Zaslavskiĭ, Georgiĭ Moiseevich
3 Aminzare, Zahra
3 Belhaq, Mohamed
...and 1,312 more Authors
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Cited in 162 Serials

131 Chaos
117 Physica D
67 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
44 Dynamical Systems
44 SIAM Journal on Applied Dynamical Systems
38 Chaos, Solitons and Fractals
30 Physics Letters. A
30 Journal of Nonlinear Science
27 Nonlinearity
25 Communications in Nonlinear Science and Numerical Simulation
20 Journal of Differential Equations
15 The Journal of Mathematical Neuroscience
9 Journal of Statistical Physics
9 Ergodic Theory and Dynamical Systems
8 Journal of Mathematical Biology
8 Physics Reports
8 Journal of Dynamics and Differential Equations
8 Nonlinear Dynamics
7 Applied Mathematics and Computation
7 Dynamics and Stability of Systems
6 Biological Cybernetics
6 Journal of Mathematical Analysis and Applications
6 Mathematical Methods in the Applied Sciences
6 Mathematics and Computers in Simulation
6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
5 Computer Methods in Applied Mechanics and Engineering
5 Transactions of the American Mathematical Society
5 Physics of Fluids
5 Journal of Difference Equations and Applications
5 Discrete and Continuous Dynamical Systems. Series B
5 Stochastics and Dynamics
5 Communications on Pure and Applied Analysis
5 Journal of Theoretical Biology
4 Geophysical and Astrophysical Fluid Dynamics
4 Journal of Fluid Mechanics
4 Physica A
4 ZAMP. Zeitschrift für angewandte Mathematik und Physik
4 Journal of Computational and Applied Mathematics
4 Proceedings of the American Mathematical Society
4 European Journal of Applied Mathematics
4 Neural Computation
4 Regular and Chaotic Dynamics
4 Nonlinear Analysis. Real World Applications
4 Mathematical Biosciences and Engineering
4 Journal of Physics A: Mathematical and Theoretical
4 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
3 Israel Journal of Mathematics
3 Mathematical Biosciences
3 Theoretical Population Biology
3 Applied Mathematical Modelling
3 SIAM Review
3 Journal of Mathematical Sciences (New York)
3 Journal of Computational Neuroscience
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 Journal of Dynamical and Control Systems
3 Qualitative Theory of Dynamical Systems
3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
2 International Journal of Modern Physics B
2 Archive for Rational Mechanics and Analysis
2 Computers & Mathematics with Applications
2 Communications in Mathematical Physics
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Bulletin of Mathematical Biology
2 Journal of Geometry and Physics
2 Automatica
2 Kybernetika
2 Applied Mathematics Letters
2 Mathematical and Computer Modelling
2 Japan Journal of Industrial and Applied Mathematics
2 International Journal of Computer Mathematics
2 Proceedings of the National Academy of Sciences of the United States of America
2 SIAM Journal on Applied Mathematics
2 Computational and Applied Mathematics
2 Discrete and Continuous Dynamical Systems
2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
2 New Journal of Physics
2 Networks and Heterogeneous Media
2 Discrete and Continuous Dynamical Systems. Series S
2 Applied General Topology
2 Journal of Applied Nonlinear Dynamics
2 Foundations of Data Science
1 Modern Physics Letters B
1 Acta Mechanica
1 American Mathematical Monthly
1 International Journal of Systems Science
1 Journal of Computational Physics
1 Journal of Mathematical Physics
1 Reports on Mathematical Physics
1 Rocky Mountain Journal of Mathematics
1 Mathematics of Computation
1 Theoretical and Computational Fluid Dynamics
1 Advances in Mathematics
1 Computing
1 International Journal of Circuit Theory and Applications
1 International Journal of Game Theory
1 Inventiones Mathematicae
1 Journal of Approximation Theory
...and 62 more Serials
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Cited in 43 Fields

512 Dynamical systems and ergodic theory (37-XX)
403 Ordinary differential equations (34-XX)
237 Biology and other natural sciences (92-XX)
140 Partial differential equations (35-XX)
44 Fluid mechanics (76-XX)
42 Numerical analysis (65-XX)
40 Mechanics of particles and systems (70-XX)
34 Combinatorics (05-XX)
32 Statistical mechanics, structure of matter (82-XX)
31 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
31 Information and communication theory, circuits (94-XX)
30 Probability theory and stochastic processes (60-XX)
29 Systems theory; control (93-XX)
22 Computer science (68-XX)
20 Geophysics (86-XX)
19 Difference and functional equations (39-XX)
15 Global analysis, analysis on manifolds (58-XX)
13 Operations research, mathematical programming (90-XX)
7 Measure and integration (28-XX)
7 Operator theory (47-XX)
7 Mechanics of deformable solids (74-XX)
7 Optics, electromagnetic theory (78-XX)
6 Integral equations (45-XX)
5 Calculus of variations and optimal control; optimization (49-XX)
5 Convex and discrete geometry (52-XX)
5 Statistics (62-XX)
5 Quantum theory (81-XX)
4 Astronomy and astrophysics (85-XX)
3 General and overarching topics; collections (00-XX)
3 Number theory (11-XX)
3 Group theory and generalizations (20-XX)
2 Commutative algebra (13-XX)
2 Functions of a complex variable (30-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 Nonassociative rings and algebras (17-XX)
1 Real functions (26-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 General topology (54-XX)
1 Algebraic topology (55-XX)

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