Glassy states and super-relaxation in populations of coupled phase oscillators

Nature Communications

Volumn 5, Issue , 2014, Pages

  Iatsenko, D ^a   McClintock, P V E ^a   Stefanovska, A ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

GLASS;

GLASS; NETWORK ANALYSIS; NUMERICAL MODEL; POPULATION STRUCTURE; RESEARCH WORK;

ARTICLE; COUPLED PHASE OSCILLATOR; DYNAMICS; KURAMOTO MODEL; MODEL; OSCILLATOR; SOLID STATE; SPECTACLES; STEADY STATE; SUPER RELAXATION;

EID: 84903154530     PISSN: None     EISSN: 20411723     Source Type: Journal    
DOI: 10.1038/ncomms5118     Document Type: Article

References (59)

1. Kuramoto, Y. Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, 1984).
2. Strogatz, S. H. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143, 1-20 (2000).
3. Acebrón, J. A., Bonilla, L. L., Vicente, C. J. P., Ritort, F. & Spigler, R. The Kuramoto model: a simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137 (2005).
4. Javaloyes, J., Perrin, M. & Politi, A. Collective atomic recoil laser as a synchronization transition. Phys. Rev. E 78, 011108 (2008).
5. Oliva, R. A. & Strogatz, S. H. Dynamics of a large array of globally coupled lasers with distributed frequencies. Int. J. Bifurcation Chaos 11, 2359-2374 (2001).
6. Breakspear, M., Heitmann, S. & Daffertshofer, A. Generative models of cortical oscillations: neurobiological implications of the Kuramoto model. Front. Hum. Neurosci. 4, 190 (2010).
7. Sheeba, J. H., Stefanovska, A. & McClintock, P. V. E. Neuronal synchrony during anesthesia: a thalamocortical model. Biophys. J. 95, 2722-2727 (2008).
8. Wiesenfeld, K., Colet, P. & Strogatz, S. H. Frequency locking in Josephson arrays: connection with the Kuramoto model. Phys. Rev. E 57, 1563-1569 (1998). (Pubitemid 128627146)
9. Néda, Z., Ravasz, E., Brechet, Y., Vicsek, T. & Barabasi, A. L. The sound of many hands clapping-tumultuous applause can transform itself into waves of synchronized clapping. Nature 403, 849-850 (2000).
10. Iatsenko, D., Petkoski, S., McClintock, P. V. E. & Stefanovska, A. Stationary and traveling wave states of the Kuramoto model with an arbitrary distribution of frequencies and coupling strengths. Phys. Rev. Lett. 110, 064101 (2013).
11. Petkoski, S. & Stefanovska, A. Kuramoto model with time-varying parameters. Phys. Rev. E 86, 046212 (2012).
12. Montbrio, E., Pazo, D. & Schmidt, J. Time delay in the Kuramoto model with bimodal frequency distribution. Phys. Rev. E 74, 056201 (2006).
13. Montbrio, E. & Pazo, D. Shear diversity prevents collective synchronization. Phys. Rev. Lett. 106, 254101 (2011).
14. Pazo, D. & Montbrio, E. The Kuramoto model with distributed shear. Europhys. Lett. 95, 60007 (2011).
15. Montbrio, E. & Pazo, D. Collective synchronization in the presence of reactive coupling and shear diversity. Phys. Rev. E 84, 046206 (2011).
16. Skardal, P. S. & Restrepo, J. G. Hierarchical synchrony of phase oscillators in modular networks. Phys. Rev. E 85, 016208 (2012).
17. Anderson, D. et al. Multiscale dynamics in communities of phase oscillators. Chaos 22, 013102 (2012).
18. Lee, W. S., Restrepo, J. G., Ott, E. & Antonsen, T. M. Dynamics and pattern formation in large systems of spatially-coupled oscillators with finite response times. Chaos 21, 023122 (2011).
19. Hong, H. & Strogatz, S. H. Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators. Phys. Rev. Lett. 106, 054102 (2011).
20. Hong, H. & Strogatz, S. H. Conformists and contrarians in a Kuramoto model with identical natural frequencies. Phys. Rev. E 84, 046202 (2011).
21. Hong, H. & Strogatz, S. H. Mean-field behavior in coupled oscillators with attractive and repulsive interactions. Phys. Rev. E 85, 056210 (2012).
22. Skardal, P. S., Ott, E. & Restrepo, J. G. Cluster synchrony in systems of coupled phase oscillators with higher-order coupling. Phys. Rev. E 84, 036208 (2011).
23. Lee, W. S., Ott, E. & Antonsen, T. M. Large coupled oscillator systems with heterogeneous interaction delays. Phys. Rev. Lett. 103, 044101 (2009).
24. Sakaguchi, H. & Kuramoto, Y. A soluble active rotator model showing phase transitions via mutual entrainment. Prog. Theor. Phys. 76, 576-581 (1986).
25. Daido, H. Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactions. Phys. Rev. Lett. 68, 1073-1076 (1992).
26. Binder, K. & Young, A. P. Spin glasses: experimental facts, theoretical concepts, and open questions. Rev. Mod. Phys. 58, 801 (1986).
27. Stein, D. L. & Newman, C. M. Spin Glasses and Complexity (Princeton University Press, 2013).
28. Vugmeister, B. & Glinchuk, M. Dipole glass and ferroelectricity in random-site electric dipole systems. Rev. Mod. Phys. 62, 993 (1990).
29. Davies, J., Lee, P. & Rice, T. Electron glass. Phys. Rev. Lett. 49, 758-761 (1982).
30. Berthier, L. & Biroli, G. Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 83, 587 (2011).
31. Daido, H. Population dynamics of randomly interacting self-oscillators. I Tractable models without frustration. Prog. Theor. Phys. 77, 622-634 (1987).
32. Bonilla, L., Perez Vicente, C. & Rubi, J. Glassy synchronization in a population of coupled oscillators. J. Stat. Phys. 70, 921-937 (1993).
33. Kloumann, I. M., Lizarraga, I. M. & Strogatz, S. H. Phase diagram for the Kuramoto model with van Hemmen interactions. Phys. Rev. E 89, 012904 (2014).
34. Stiller, J. C. & Radons, G. Dynamics of nonlinear oscillators with random interactions. Phys. Rev. E 58, 1789 (1998).
35. Daido, H. Algebraic relaxation of an order parameter in randomly coupled limit-cycle oscillators. Phys. Rev. E 61, 2145 (2000).
36. Stiller, J. C. & Radons, G. Self-averaging of an order parameter in randomly coupled limit-cycle oscillators. Phys. Rev. E 61, 2148 (2000).
37. Pikovsky, A. & Rosenblum, M. Partially integrable dynamics of hierarchical populations of coupled oscillators. Phys. Rev. Lett. 101, 264103 (2008).
38. Pikovsky, A. & Rosenblum, M. Dynamics of heterogeneous oscillator ensembles in terms of collective variables. Physica D 240, 872-881 (2011).
39. Ott, E. & Antonsen, T. M. Long time evolution of phase oscillator systems. Chaos 19, 023117 (2009).
40. Ott, E., Hunt, B. R. & Antonsen, T. M. Comment on 'Long time evolution of phase oscillator systems' [Chaos 19, 023117 (2009)]. Chaos 21, 025112 (2011).
41. Ott, E. & Antonsen, T. M. Low dimensional behavior of large systems of globally coupled oscillators. Chaos 18, 037113 (2008).
42. Petkoski, S., Iatsenko, D., Basnarkov, L. & Stefanovska, A. Mean-field and mean-ensemble frequencies of a system of coupled oscillators. Phys. Rev. E 87, 032908 (2013).
43. Marvel, S. A., Mirollo, R. E. & Strogatz, S. H. Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action. Chaos 19, 043104 (2009).
44. Yuan, D., Zhang, M. & Yang, J. Dynamics of the Kuramoto model in the presence of correlation between distributions of frequencies and coupling strengths. Phys. Rev. E 89, 012910 (2014).
45. Strogatz, S. H. & Mirollo, R. E. Stability of incoherence in a population of coupled oscillators. J. Stat. Phys. 63, 613-635 (1991).
46. Omelchenko, E. & Wolfrum, M. Nonuniversal transitions to synchrony in the Sakaguchi-Kuramoto model. Phys. Rev. Lett. 109, 164101 (2012).
47. Omelchenko, O. E. & Wolfrum, M. Bifurcations in the Sakaguchi-Kuramoto model. Physica D 263, 74-85 (2013).
48. Hagerstrom, A. M. et al. Experimental observation of chimeras in coupled-map lattices. Nat. Phys. 8, 658-661 (2012).
49. Tinsley, M. R., Nkomo, S. & Showalter, K. Chimera and phase-cluster states in populations of coupled chemical oscillators. Nat. Phys. 8, 662-665 (2012).
50. Mattis, D. Solvable spin systems with random interactions. Phys. Lett. A 56, 421-422 (1976).
51. Amit, D. J., Gutfreund, H. & Sompolinsky, H. Storing infinite numbers of patterns in a spin-glass model of neural networks. Phys. Rev. Lett. 55, 1530 (1985).
52. Amit, D. J., Gutfreund, H. & Sompolinsky, H. Spin-glass models of neural networks. Phys. Rev. A 32, 1007 (1985).
53. Villain, J. Insulating spin glasses. Z. Phys. B 33, 31-42 (1979).
54. Daido, H. Multibranch entrainment and scaling in large populations of coupled oscillators. Phys. Rev. Lett. 77, 1406 (1996).
55. Martens, E. A. et al. Exact results for the Kuramoto model with a bimodal frequency distribution. Phys. Rev. E 79, 026204 (2009).
56. Pikovsky, A. & Rosenblum, M. Self-organized partially synchronous dynamics in populations of nonlinearly coupled oscillators. Physica D 238, 27-37 (2009).
57. Filatrella, G., Pedersen, N. F. & Wiesenfeld, K. Generalized coupling in the Kuramoto model. Phys. Rev. E 75, 017201 (2007).
58. Rosenblum, M. & Pikovsky, A. Self-organized quasiperiodicity in oscillator ensembles with global nonlinear coupling. Phys. Rev. Lett. 98, 064101 (2007).
59. Baibolatov, Y., Rosenblum, M., Zhanabaev, Z. Z. & Pikovsky, A. Complex dynamics of an oscillator ensemble with uniformly distributed natural frequencies and global nonlinear coupling. Phys. Rev. E 82, 016212 (2010).