Mean-field theory revives in self-oscillatory fields with non-local couplingReport as inadecuate

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Published in: Progress of theoretical physics supplement, vol. 161, p. 127-143 Publication date: 2006

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 disscuss 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 peciliar 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.

Keywords: mean-field theory ; limit cycle oscillators ; nonlocal coupling Reference LANOS-ARTICLE-2008-021doi:10.1143/PTPS.161.127

Author: Kuramoto, Yoshiki; Shima, Shin-ichiro; Battogtoch, Dorjsuren; Shiogai, Yuri


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