Emergent collective behaviors of stochastic kuramoto oscillators

Seung-Yeal Ha, ,Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 00826, Korea (Republic of), Dongnam Ko, Chanho Min, Xiongtao Zhang, ,Korea Institute for Advanced Study, Hoegiro 85, Seoul 02455, Korea (Republic of), ,DeustoTech, University of Deusto, and Facultad de Ingeniería, Universidad de Deusto, Avenida de las Universidades 24, Bilbao 48007, Basque Country, Spain, ,Department of Mathematical Sciences, Seoul National University, Seoul 00826, Korea (Republic of), ,Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan, Hubei Province, China
2017 Discrete and continuous dynamical systems. Series B  
We study the collective dynamics of Kuramoto ensemble under uncertain coupling strength. For a finite ensemble, we can model the dynamics of the Kuramoto ensemble by the stochastic Kuramoto system with multiplicative noise. In contrast, for an infinite ensemble, the dynamics is effectively described by the Kuramoto-Sakaguchi-Fokker-Planck(KS-FP) equation with state dependent degenerate diffusion. We present emergent synchronization estimates for the stochastic and kinetic models, which yield
more » ... stability of the phase-locked state for identical Kuramoto ensemble with the same natural frequencies. We also provide a brief explanation on the mean-field limit between two models. 2010 Mathematics Subject Classification. Primary: 92B25, 93E15; Secondary: 70K20.
doi:10.3934/dcdsb.2019208 fatcat:jwkfnk5yebfcpfljwludrnszly