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Progress of Theoretical Physics
Supplement No.161 (2006) pp. 127-143
URL : http://ptp.ipap.jp/link?PTPS/161/127/
DOI : 10.1143/PTPS.161.127

Mean-Field Theory Revives in Self-Oscillatory Fields with Non-Local Coupling

Yoshiki Kuramoto,1 Shin-ichiro Shima,2 Dorjsuren Battogtokh3 and Yuri Shiogai4

1Department of Mathematics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
2The Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan
3Department of Biology, Virginia Polytechnic and State University, Blacksburg, Virginia 24061, USA
4Department of Physics, Lancaster University, Lancaster LA1 4YB, UK

(Received July 17, 2005)

A simple mean-field idea is applicable to the pattern dynamics of large assemblies of limit-cycle oscillators with non-local coupling. This is demonstrated by developing a mathematical theory for the following two specific examples of pattern dynamics. Firstly, we discuss propagation of phase waves in noisy oscillatory media, with particular concern with the existence of a critical condition for persistent propagation of the waves throughout the medium, and also with the possibility of noise-induced turbulence. Secondly, we discuss the existence of an exotic class of patterns peculiar to non-local coupling called chimera where the system is composed of two distinct domains, one coherent and the other incoherent, separated from each other with sharp boundaries.


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