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Volumn 240, Issue 24, 2011, Pages 1960-1971

Fronts and bumps in spatially extended Kuramoto networks

Author keywords

Bifurcation; Fronts; Kuramoto; Non local; Phase oscillators; Synchrony

Indexed keywords

BIFURCATION (MATHEMATICS); PHYSICS;

EID: 80055053634     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2011.09.009     Document Type: Article
Times cited : (83)

References (47)
  • 4
    • 0039592729 scopus 로고    scopus 로고
    • From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators
    • S.H. Strogatz From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators Physica D 143 2000 1 20
    • (2000) Physica D , vol.143 , pp. 1-20
    • Strogatz, S.H.1
  • 5
    • 19944385353 scopus 로고    scopus 로고
    • The Kuramoto model: A simple paradigm for synchronization phenomena
    • DOI 10.1103/RevModPhys.77.137
    • J.A. Acebrón, L.L. Bonilla, C.J. Pérez Vicente, F. Ritort, and R. Spigler The Kuramoto model: a simple paradigm for synchronization phenomena Rev. Modern Phys. 77 2005 137 185 (Pubitemid 41490657)
    • (2005) Reviews of Modern Physics , vol.77 , Issue.1 , pp. 137-185
    • Acebron, J.A.1    Bonilla, L.L.2    Vicente, C.J.P.3    Ritort, F.4    Spigler, R.5
  • 6
    • 58149359407 scopus 로고    scopus 로고
    • Partially integrable dynamics of hierarchical populations of coupled oscillators
    • Arkady Pikovsky, and Michael Rosenblum Partially integrable dynamics of hierarchical populations of coupled oscillators Phys. Rev. Lett. 101 2008 264103
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 264103
    • Pikovsky, A.1    Rosenblum, M.2
  • 7
    • 74349098541 scopus 로고    scopus 로고
    • Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action
    • S.A. Marvel, R.E. Mirollo, and S.H. Strogatz Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action Chaos 19 2009 043104
    • (2009) Chaos , vol.19 , pp. 043104
    • Marvel, S.A.1    Mirollo, R.E.2    Strogatz, S.H.3
  • 8
    • 54749126999 scopus 로고    scopus 로고
    • Low dimensional behavior of large systems of globally coupled oscillators
    • Edward Ott, and Thomas M. Antonsen Low dimensional behavior of large systems of globally coupled oscillators Chaos 18 2008 037113
    • (2008) Chaos , vol.18 , pp. 037113
    • Ott, E.1    Antonsen, T.M.2
  • 9
    • 50249167155 scopus 로고    scopus 로고
    • Solvable model for chimera states of coupled oscillators
    • Daniel M. Abrams, Rennie Mirollo, Steven H. Strogatz, and Daniel A. Wiley Solvable model for chimera states of coupled oscillators Phys. Rev. Lett. 101 2008 084103
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 084103
    • Abrams, D.M.1    Mirollo, R.2    Strogatz, S.H.3    Wiley, D.A.4
  • 11
    • 47249127645 scopus 로고    scopus 로고
    • Partially locked states in coupled oscillators due to inhomogeneous coupling
    • T.W. Ko, and G.B. Ermentrout Partially locked states in coupled oscillators due to inhomogeneous coupling Phys. Rev. E 78 1 2008 016203
    • (2008) Phys. Rev. e , vol.78 , Issue.1 , pp. 016203
    • Ko, T.W.1    Ermentrout, G.B.2
  • 12
    • 0032353077 scopus 로고    scopus 로고
    • Monotonicity of phaselocked solutions in chains and arrays of nearest-neighbor coupled oscillators
    • L. Ren, and B. Ermentrout Monotonicity of phaselocked solutions in chains and arrays of nearest-neighbor coupled oscillators SIAM J. Math. Anal. 29 1 1998 208 234
    • (1998) SIAM J. Math. Anal. , vol.29 , Issue.1 , pp. 208-234
    • Ren, L.1    Ermentrout, B.2
  • 13
    • 28844506120 scopus 로고    scopus 로고
    • Collective synchronization in spatially extended systems of coupled oscillators with random frequencies
    • H. Hong, Hyunggyu Park, and M.Y. Choi Collective synchronization in spatially extended systems of coupled oscillators with random frequencies Phys. Rev. E 72 3 2005 036217
    • (2005) Phys. Rev. e , vol.72 , Issue.3 , pp. 036217
    • Hong, H.1    Park, H.2    Choi, M.Y.3
  • 14
    • 42749099087 scopus 로고    scopus 로고
    • Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators
    • S. Shima, and Y. Kuramoto Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators Phys. Rev. E 69 3 2004 036213
    • (2004) Phys. Rev. e , vol.69 , Issue.3 , pp. 036213
    • Shima, S.1    Kuramoto, Y.2
  • 15
    • 0035403248 scopus 로고    scopus 로고
    • Stationary bumps in networks of spiking neurons
    • DOI 10.1162/089976601750264974
    • C.R. Laing, and C.C. Chow Stationary bumps in networks of spiking neurons Neural Comput. 13 2001 1473 1494 (Pubitemid 33595029)
    • (2001) Neural Computation , vol.13 , Issue.7 , pp. 1473-1494
    • Laing, C.R.1    Chow, C.C.2
  • 16
    • 0032570706 scopus 로고    scopus 로고
    • Propagating activity patterns in large-scale inhibitory neuronal networks
    • J. Rinzel, D. Terman, X.J. Wang, and B. Ermentrout Propagating activity patterns in large-scale inhibitory neuronal networks Science 279 5355 1998 1351
    • (1998) Science , vol.279 , Issue.5355 , pp. 1351
    • Rinzel, J.1    Terman, D.2    Wang, X.J.3    Ermentrout, B.4
  • 17
    • 2542504827 scopus 로고    scopus 로고
    • Coexistence of coherence and incoherence in nonlocally coupled phase oscillators
    • Y. Kuramoto, and D. Battogtokh Coexistence of coherence and incoherence in nonlocally coupled phase oscillators Nonlinear Phenom. Complex Syst. 5 2002 380 385
    • (2002) Nonlinear Phenom. Complex Syst. , vol.5 , pp. 380-385
    • Kuramoto, Y.1    Battogtokh, D.2
  • 18
    • 41349107163 scopus 로고    scopus 로고
    • Pattern formation in a two-dimensional array of oscillators with phase-shifted coupling
    • P.J. Kim, T.W. Ko, H. Jeong, and H.T. Moon Pattern formation in a two-dimensional array of oscillators with phase-shifted coupling Phys. Rev. E 70 6 2004 065201
    • (2004) Phys. Rev. e , vol.70 , Issue.6 , pp. 065201
    • Kim, P.J.1    Ko, T.W.2    Jeong, H.3    Moon, H.T.4
  • 19
    • 77954003394 scopus 로고    scopus 로고
    • Chimera states as chaotic spatiotemporal patterns
    • Oleh E. Omel'chenko, Matthias Wolfrum, and Yuri L. Maistrenko Chimera states as chaotic spatiotemporal patterns Phys. Rev. E 81 6 2010 065201
    • (2010) Phys. Rev. e , vol.81 , Issue.6 , pp. 065201
    • Omel'Chenko, O.E.1    Wolfrum, M.2    Maistrenko, Y.L.3
  • 21
    • 67650096320 scopus 로고    scopus 로고
    • The dynamics of chimera states in heterogeneous Kuramoto networks
    • C. Laing The dynamics of chimera states in heterogeneous Kuramoto networks Physica D 238 2009 1569 1588
    • (2009) Physica D , vol.238 , pp. 1569-1588
    • Laing, C.1
  • 22
    • 19744381710 scopus 로고    scopus 로고
    • Chimera states for coupled oscillators
    • Daniel M. Abrams, and Steven H. Strogatz Chimera states for coupled oscillators Phys. Rev. Lett. 93 2004 174102
    • (2004) Phys. Rev. Lett. , vol.93 , pp. 174102
    • Abrams, D.M.1    Strogatz, S.H.2
  • 23
    • 33644921219 scopus 로고    scopus 로고
    • Chimera states in a ring of nonlocally coupled oscillators
    • DOI 10.1142/S0218127406014551, PII S0218127406014551
    • Daniel M. Abrams, and Steven H. Strogatz Chimera states in a ring of nonlocally coupled oscillators Internat. J. Bifur. Chaos 16 2006 21 37 (Pubitemid 43383889)
    • (2006) International Journal of Bifurcation and Chaos , vol.16 , Issue.1 , pp. 21-37
    • Abrams, D.M.1    Strogatz, S.H.2
  • 24
    • 42149089007 scopus 로고    scopus 로고
    • Clustered chimera states in delay-coupled oscillator systems
    • G.C. Sethia, A. Sen, and F.M. Atay Clustered chimera states in delay-coupled oscillator systems Phys. Rev. Lett. 100 2008 144102
    • (2008) Phys. Rev. Lett. , vol.100 , pp. 144102
    • Sethia, G.C.1    Sen, A.2    Atay, F.M.3
  • 25
    • 63849150175 scopus 로고    scopus 로고
    • Chimera states in heterogeneous networks
    • Carlo R. Laing Chimera states in heterogeneous networks Chaos 19 2009 013113
    • (2009) Chaos , vol.19 , pp. 013113
    • Laing, C.R.1
  • 26
    • 34347213091 scopus 로고    scopus 로고
    • Chimera Ising walls in forced nonlocally coupled oscillators
    • Y. Kawamura Chimera Ising walls in forced nonlocally coupled oscillators Phys. Rev. E 75 5 2007 056204
    • (2007) Phys. Rev. e , vol.75 , Issue.5 , pp. 056204
    • Kawamura, Y.1
  • 27
    • 78650681474 scopus 로고    scopus 로고
    • Self-emerging and turbulent chimeras in oscillator chains
    • G. Bordyugov, A. Pikovsky, and M. Rosenblum Self-emerging and turbulent chimeras in oscillator chains Phys. Rev. E 82 3 2010 035205
    • (2010) Phys. Rev. e , vol.82 , Issue.3 , pp. 035205
    • Bordyugov, G.1    Pikovsky, A.2    Rosenblum, M.3
  • 29
    • 38849086596 scopus 로고    scopus 로고
    • Chimera states: The natural link between coherence and incoherence
    • O.E. Omel'chenko, Y.L. Maistrenko, and P.A. Tass Chimera states: the natural link between coherence and incoherence Phys. Rev. Lett. 100 2008 044105
    • (2008) Phys. Rev. Lett. , vol.100 , pp. 044105
    • Omel'Chenko, O.E.1    Maistrenko, Y.L.2    Tass, P.A.3
  • 30
    • 67651092270 scopus 로고    scopus 로고
    • Long time evolution of phase oscillator systems
    • E. Ott, and T.M. Antonsen Long time evolution of phase oscillator systems Chaos 19 2009 023117
    • (2009) Chaos , vol.19 , pp. 023117
    • Ott, E.1    Antonsen, T.M.2
  • 31
    • 79959990554 scopus 로고    scopus 로고
    • Dynamics and pattern formation in large systems of spatially-coupled oscillators with finite response times
    • Wai Shing Lee, Juan G. Restrepo, Edward Ott, and Thomas M. Antonsen Dynamics and pattern formation in large systems of spatially-coupled oscillators with finite response times Chaos 21 2 2011 023122
    • (2011) Chaos , vol.21 , Issue.2 , pp. 023122
    • Lee, W.S.1    Restrepo, J.G.2    Ott, E.3    Antonsen, T.M.4
  • 32
    • 79551643808 scopus 로고    scopus 로고
    • Kuramoto model of coupled oscillators with positive and negative coupling parameters: An example of conformist and contrarian oscillators
    • Hyunsuk Hong, and Steven H. Strogatz Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators Phys. Rev. Lett. 106 5 2011 054102
    • (2011) Phys. Rev. Lett. , vol.106 , Issue.5 , pp. 054102
    • Hong, H.1    Strogatz, S.H.2
  • 33
    • 3042573558 scopus 로고    scopus 로고
    • Freezing solutions of equivariant evolution equations
    • W.J. Beyn, and V. Thmmler Freezing solutions of equivariant evolution equations SIAM J. Appl. Dyn. Syst. 3 2 2004 85 116
    • (2004) SIAM J. Appl. Dyn. Syst. , vol.3 , Issue.2 , pp. 85-116
    • Beyn, W.J.1    Thmmler, V.2
  • 35
    • 68649086672 scopus 로고    scopus 로고
    • Large coupled oscillator systems with heterogeneous interaction delays
    • W.S. Lee, E. Ott, and T.M. Antonsen Large coupled oscillator systems with heterogeneous interaction delays Phys. Rev. Lett. 103 4 2009 44101
    • (2009) Phys. Rev. Lett. , vol.103 , Issue.4 , pp. 44101
    • Lee, W.S.1    Ott, E.2    Antonsen, T.M.3
  • 36
    • 0000654735 scopus 로고    scopus 로고
    • Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
    • PII S0167278997002091
    • A.R. Champneys Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics Physica D 112 12 1998 158 186 (Pubitemid 128676463)
    • (1998) Physica D: Nonlinear Phenomena , vol.112 , Issue.1-2 , pp. 158-186
    • Champneys, A.R.1
  • 40
    • 35748962631 scopus 로고    scopus 로고
    • Bumps and rings in a two-dimensional neural field: Splitting and rotational instabilities
    • M.R. Owen, C.R. Laing, and S. Coombes Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities New J. Phys. 9 2007 378
    • (2007) New J. Phys. , vol.9 , pp. 378
    • Owen, M.R.1    Laing, C.R.2    Coombes, S.3
  • 41
    • 58149347754 scopus 로고    scopus 로고
    • Stability diagram for the forced Kuramoto model
    • Lauren M. Childs, and Steven H. Strogatz Stability diagram for the forced Kuramoto model Chaos 18 4 2008 043128
    • (2008) Chaos , vol.18 , Issue.4 , pp. 043128
    • Childs, L.M.1    Strogatz, S.H.2
  • 42
    • 50249121924 scopus 로고    scopus 로고
    • Bistability between synchrony and incoherence in limit-cycle oscillators with coupling strength inhomogeneity
    • Tae-Wook Ko, and G. Bard Ermentrout Bistability between synchrony and incoherence in limit-cycle oscillators with coupling strength inhomogeneity Phys. Rev. E 78 2 2008 026210
    • (2008) Phys. Rev. e , vol.78 , Issue.2 , pp. 026210
    • Ko, T.-W.1    Ermentrout, G.B.2
  • 43
    • 79959999889 scopus 로고    scopus 로고
    • Comment on "long time evolution of phase oscillator systems" [Chaos 19, 023117, (2009)]
    • Edward Ott, Brian R. Hunt, and Thomas M. Antonsen Jr. Comment on "long time evolution of phase oscillator systems" [Chaos 19, 023117, (2009)] Chaos 21 2 2011 025112
    • (2011) Chaos , vol.21 , Issue.2 , pp. 025112
    • Ott, E.1    Hunt, B.R.2    Antonsen, Jr.T.M.3
  • 44
    • 23944523647 scopus 로고    scopus 로고
    • Spiral waves in nonlocal equations
    • DOI 10.1137/040612890
    • C.R. Laing Spiral waves in nonlocal equations SIAM J. Appl. Dyn. Syst. 4 3 2005 588 606 (Pubitemid 43385167)
    • (2005) SIAM Journal on Applied Dynamical Systems , vol.4 , Issue.3 , pp. 588-606
    • Laing, C.R.1
  • 45
    • 35949003696 scopus 로고    scopus 로고
    • Modeling electrocortical activity through improved local approximations of integral neural field equations
    • S. Coombes, N.A. Venkov, L. Shiau, I. Bojak, D.T.J. Liley, and C.R. Laing Modeling electrocortical activity through improved local approximations of integral neural field equations Phys. Rev. E 76 5 2007 051901
    • (2007) Phys. Rev. e , vol.76 , Issue.5 , pp. 051901
    • Coombes, S.1    Venkov, N.A.2    Shiau, L.3    Bojak, I.4    Liley, D.T.J.5    Laing, C.R.6
  • 46
    • 60149105197 scopus 로고    scopus 로고
    • Transient Turing patterns in a neural field model
    • A.J. Elvin, C.R. Laing, and M.G. Roberts Transient Turing patterns in a neural field model Phys. Rev. E 79 1 2009 011911
    • (2009) Phys. Rev. e , vol.79 , Issue.1 , pp. 011911
    • Elvin, A.J.1    Laing, C.R.2    Roberts, M.G.3
  • 47
    • 77951749327 scopus 로고    scopus 로고
    • Spontaneous synchronization of coupled oscillator systems with frequency adaptation
    • D. Taylor, E. Ott, and J.G. Restrepo Spontaneous synchronization of coupled oscillator systems with frequency adaptation Phys. Rev. E 81 4 2010 046214
    • (2010) Phys. Rev. e , vol.81 , Issue.4 , pp. 046214
    • Taylor, D.1    Ott, E.2    Restrepo, J.G.3


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