Dynamics of heterogeneous oscillator ensembles in terms of collective variables

Physica D: Nonlinear Phenomena

Volumn 240, Issue 9-10, 2011, Pages 872-881

  Pikovsky, Arkady ^a   Rosenblum, Michael ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Coupled oscillators; Kuramoto model; Nonlinear coupling; Oscillator ensembles; OttAntonsen theory; WatanabeStrogatz theory

Indexed keywords

OSCILLATORS (ELECTRONIC); SYNCHRONIZATION;

COUPLED OSCILLATORS; KURAMOTO MODELS; NONLINEAR COUPLING; OSCILLATOR ENSEMBLES; OTTANTONSEN THEORY; WATANABESTROGATZ THEORY;

DYNAMICS;

EID: 79952454546     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2011.01.002     Document Type: Article

References (53)

1. K. Wiesenfeld, and J.W. Swift Averaged equations for Josephson junction series arrays Phys. Rev. E 51 2 1995 1020 1025
2. A.F. Glova Phase locking of optically coupled lasers Quantum Electron. 33 4 2003 283 306
3. I.Z. Kiss, Y. Zhai, and J.L. Hudson Emerging coherence in a population of chemical oscillators Science 296 2002 1676 1678 (Pubitemid 34579162)
4. S.H. Strogatz, D.M. Abrams, A. McRobie, B. Eckhardt, and E. Ott Theoretical mechanics: crowd synchrony on the millennium bridge Nature 438 2005 43 44 (Pubitemid 41599813)
5. B. Eckhardt, E. Ott, S.H. Strogatz, D.M. Abrams, and A. McRobie Modeling walker synchronization on the millennium bridge Phys. Rev. E 75 2007 021110
6. Z. Nda, E. Ravasz, Y. Brechet, T. Vicsek, and A.-L. Barabsi Tumultuous applause can transform itself into waves of synchronized clapping Nature 403 6772 2000 849 850
7. P. Richard, B.M. Bakker, B. Teusink, K. Van Dam, and H.V. Westerhoff Acetaldehyde mediates the synchronization of sustained glycolytic oscillations in population of yeast cells Eur. J. Biochem. 235 1996 238 241 (Pubitemid 26048625)
8. S. Dano, P.G. Sorensen, and F. Hynne Sustained oscillations in living cells Nature 402 6759 1999 320 322 (Pubitemid 129516271)
9. D. Gonze, N. Markadieu, and A. Goldbeter Selection of in-phase or out-of-phase synchronization in a model based on global coupling of cells undergoing metabolic oscillations Chaos 18 3 2008 037127
10. D. Golomb, D. Hansel, and G. Mato Mechanisms of synchrony of neural activity in large networks F. Moss, S. Gielen, Neuro-Informatics and Neural Modeling Handbook of Biological Physics vol. 4 2001 Elsevier Amsterdam 887 968
11. H. Sakaguchi Cooperative phenomena in coupled oscillator systems under external fields Progr. Theoret. Phys. 79 1 1988 39 46
12. T.M. Antonsen Jr., R.T. Faghih, M. Girvan, E. Ott, and J. Platig External periodic driving of large systems of globally coupled phase oscillators Chaos 18 3 2008 037112
13. P.A. Tass Phase Resetting in Medicine and Biology. Stochastic Modelling and Data Analysis 1999 Springer-Verlag Berlin
14. M. Rosenblum, and A. Pikovsky Controlling synchronization in an ensemble of globally coupled oscillators Phys. Rev. Lett. 92 11 2004 114102
15. M. Rosenblum, and A. Pikovsky Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms Phys. Rev. E 70 2004 041904
16. L.M. Childs, and S.H. Strogatz Stability diagram for the forced Kuramoto model Chaos 18 4 2008 043128
17. E.A. Martens, E. Barreto, S.H. Strogatz, E. Ott, P. So, and T.M. Antonsen Exact results for the Kuramoto model with a bimodal frequency distribution Phys. Rev. E 79 2 2009 026204
18. D.M. Abrams, R. Mirollo, S.H. Strogatz, and D.A. Wiley Solvable model for chimera states of coupled oscillators Phys. Rev. Lett. 101 2008 084103
19. O.E. Omel'chenko, Yu.L. Maistrenko, and P.A. Tass Chimera states: the natural link between coherence and incoherence Phys. Rev. Lett. 100 4 2008 044105
20. C.R. Laing The dynamics of chimera states in heterogeneous Kuramoto networks Physica D 238 16 2009 1569 1588
21. M. Rosenblum, and A. Pikovsky Self-organized quasiperiodicity in oscillator ensembles with global nonlinear coupling Phys. Rev. Lett. 98 2007 064101
22. A. Pikovsky, and M. Rosenblum Self-organized partially synchronous dynamics in populations of nonlinearly coupled oscillators Physica D 238 1 2009 27 37
23. E. Ott, and Th.M. Antonsen Low dimensional behavior of large systems of globally coupled oscillators Chaos 18 3 2008 037113
24. E. Ott, and Th.M. Antonsen Long time evolution of phase oscillator systems Chaos 19 2 2009 023117
25. D. Pao Thermodynamic limit of the first-order phase transition in the Kuramoto model Phys. Rev. E 72 4, Part 2 2005 046211
26. D. Paz, and E. Montbri Existence of hysteresis in the Kuramoto model with bimodal frequency distributions Phys. Rev. E 80 4 2009 046215
27. H. Kori, and Y. Kuramoto Slow switching in globally coupled oscillators: robustness and occurrence through delayed coupling Phys. Rev. E 63 2001 046214
28. Z. Liu, Y.-C. Lai, and F.C. Hoppensteadt Phase clustering and transition to phase synchronization in a large number of coupled nonlinear oscillators Phys. Rev. E 63 5 2001 055201
29. Yu. Maistrenko, O. Popovych, O. Burylko, and P.A. Tass Mechanism of desynchronization in the finite-dimensional Kuramoto model Phys. Rev. Lett. 93 8 2004 084102
30. Y. Kuramoto Self-entrainment of a population of coupled nonlinear oscillators H. Araki, International Symposium on Mathematical Problems in Theoretical Physics Lecture Notes Phys. vol. 39 1975 Springer New York 420
31. Y. Kuramoto Chemical Oscillations, Waves and Turbulence 1984 Springer Berlin
32. H. Daido Order function and macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators Progr. Theoret. Phys. 88 6 1992 1213 1218
33. H. Daido Critical conditions of macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators Progr. Theoret. Phys. 89 4 1993 929 934
34. H. Daido Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions: bifurcation of the order function Physica D 91 1996 24 66 (Pubitemid 126687303)
35. H. Sakaguchi, and Y. Kuramoto A soluble active rotator model showing phase transition via mutual entrainment Progr. Theoret. Phys. 76 3 1986 576 581
36. A. Pikovsky, M. Rosenblum, and J. Kurths Synchronization. A Universal Concept in Nonlinear Sciences 2001 Cambridge University Press Cambridge
37. J.A. Acebron, L.L. Bonilla, C.J. Perez Vicente, F. Ritort, and R. Spigler The Kuramoto model: a simple paradigm for synchronization phenomena Rev. Modern Phys. 77 1 2005 137 175
38. S.H. Strogatz From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators Physica D 143 14 2000 1 20
39. G. Filatrella, N.F. Pedersen, and K. Wiesenfeld Generalized coupling in the Kuramoto model Phys. Rev. E 75 2007 017201
40. F. Giannuzzi, D. Marinazzo, G. Nardulli, M. Pellicoro, and S. Stramaglia Phase diagram of a generalized winfree model Phys. Rev. E 75 2007 051104
41. S. Watanabe, and S.H. Strogatz Integrability of a globally coupled oscillator array Phys. Rev. Lett. 70 16 1993 2391 2394
42. S. Watanabe, and S.H. Strogatz Constants of motion for superconducting Josephson arrays Physica D 74 1994 197 253
43. A. Pikovsky, and M. Rosenblum Partially integrable dynamics of hierarchical populations of coupled oscillators Phys. Rev. Lett. 101 2008 2264103
44. S.A. Marvel, R.E. Mirollo, and S.H. Strogatz Phase oscillators with global sinusoidal coupling evolve by Mobius group action Chaos 19 2009 043104
45. W.S. Lee, E. Ott, and T.M. Antonsen Large coupled oscillator systems with heterogeneous interaction delays Phys. Rev. Lett. 103 4 2009 044101
46. M.M. Abdulrehem, and E. Ott Low dimensional description of pedestrian-induced oscillation of the millennium bridge Chaos 19 2009 013129
47. H. Daido Multi-branch entrainment and multi-peaked order-functions in a phase model of limit-cycle oscillators with uniform all-to-all coupling J. Phys. A: Math. Gen. 28 1995 L151 L157
48. S.A. Marvel, and S.H. Strogatz Invariant submanifold for series arrays of Josephson junctions Chaos 19 2009 013132
49. Y. Baibolatov, M. Rosenblum, Z.Zh. Zhanabaev, and A. Pikovsky Complex dynamics of an oscillator ensemble with uniformly distributed natural frequencies and global nonlinear coupling Phys. Rev. E 82 1 2010 016212
50. E. Ott, J.H. Platig, T.M. Antonsen, and M. Girvan Echo phenomena in large systems of coupled oscillators Chaos 18 3 2008 037115
51. Y. Kuramoto, and D. Battogtokh Coexistence of coherence and incoherence in nonlocally coupled phase oscillators Nonlinear Phenom. Complex Syst. 5 2002 380 385
52. D.M. Abrams, and S.H. Strogatz Chimera states for coupled oscillators Phys. Rev. Lett. 93 17 2004 174102
53. G. Bordyugov, A. Pikovsky, and M. Rosenblum Self-emerging and turbulent chimeras in oscillator chains Phys. Rev. E 82 3 2010 035205