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External Noise Can Cause Complex Effective Dynamics in Pattern-Forming Systems
Yoshiki Kuramoto,Yoji Kawamura 한국물리학회 2007 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.50 No.1I
To demonstrate how nonlocally coupled oscillator systems can precisely be handled theoretically, we study a particular class of phenomena in which external noise generates complex effective dynamics in spatially uniform systems. The systems studied are large assemblies of oscillators with nonlocal coupling, and a theory is presented to explain this counter-intuitive behavior. Our theory is based on the phase reduction method, which is applied twice, i.e., firstly for eliminating all degrees of freedom other than phase and secondly for transforming a stochastic phase equation to an equation governing the order parameter phase. The validity of our theory is confirmed by a comparison with numerical simulations.m