Kuramoto, YoshikiShima, Shin-ichiroBattogtoch, DorjsurenShiogai, Yuri2008-02-142008-02-142008-02-14200610.1143/PTPS.161.127https://infoscience.epfl.ch/handle/20.500.14299/18313A 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.mean-field theorylimit cycle oscillatorsnonlocal couplingtext::journal::journal article::research article