There is no non-zero stable fixed point for dense networks in the homogeneous Kuramoto model

Journal of Physics A: Mathematical and Theoretical

Volumn 45, Issue 5, 2012, Pages

  Taylor, Richard ^a  

^a DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84856264719     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/45/5/055102     Document Type: Article

References (13)

1. Acebron J A, Bonilla L L, Perez Vincente C J, Ritort F and Spigler R 2005 The Kuramoto model: a simple paradigm for synchronization phenomena Rev. Mod. Phys. 77 13785 (Pubitemid 41490657)
2. Arenas A, Diaz-Guilera A, Kurths J, Moreno Y and Zhou C 2008 Synchronization in complex networks Phys. Rep. 469 93153
3. Boccaletti S, Latora V, Moreno Y, Chavez M and Hwang D U 2006 Complex networks: structure and dynamics Phys. Rep. 424 175308 (Pubitemid 43135890)
4. Bondy J A and Murty U S R 1976 Graph Theory with Applications (London: Macmillan)
5. Diaz-Guilera A and Arenas A 2008 Phase patterns of coupled oscillators with application to wireless communication BIOWIRE 2007 (Cambridge, UK) ed P Lio (Berlin: Springer) pp 17279
6. Dorogovstev S N, Goltsev A V and Mendes J F F 2008 Critical phenomena in complex networks Rev. Mod. Phys. 80 1275335
7. Jadbabauie A, Motee N and Barahona M 2004 On the stability of the Kuramoto model of coupled nonlinear oscillators Proc. of the American Control Conf. p 4296
8. Kuramoto Y 1975 Self-entrainment of a population of coupled nonlinear oscillators Int. Symp. on Mathematical Problems in Theoretical Physics (Lecture Notes in Physics vol 39) ed H Araki (New York: Springer) pp 4202
9. Lorenz E N 1996 The Essence of Chaos (The Jessie and John Danz Lecture Series) (Washington, DC: University of Washington Press)
10. Ochab J and Gora P F 2010 Synchronization of coupled oscillators in a local one-dimensional Kuramoto model Summer Solstice 2009: Int. Conf. on Discrete Models of Complex Systems Acta Phys. Pol. Proc. Suppl. B 3 pp 453-462
11. Strogatz S H 2000 From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators Physica D 143 120
12. Verwoerd M and Mason O 2007 Conditions for the existence of fixed points in a finite system of Kuramoto oscillators Proc. of the American Control Conf. pp 46138
13. Wiley D A, Strogatz S H and Girvan M 2006 The size of the synch basin Chaos 16 015103