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Dynamics and Pattern Formation in Large Systems of Spatially-Coupled Oscillators with Finite Response Times

By Wai Shing Lee, Juan G. Restrepo, Edward Ott and Thomas M. Antonsen

Abstract

We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from other oscillators in its neighborhood. Using the ansatz of Ott and Antonsen (Ref. \cite{OA1}) and adopting a strategy similar to that employed in the recent work of Laing (Ref. \cite{Laing2}), we reduce the microscopic dynamics of these systems to a macroscopic partial-differential-equation description. Using this macroscopic formulation, we numerically find that finite oscillator response time leads to interesting spatio-temporal dynamical behaviors including propagating fronts, spots, target patterns, chimerae, spiral waves, etc., and we study interactions and evolutionary behaviors of these spatio-temporal patterns

Topics: Nonlinear Sciences - Pattern Formation and Solitons, Nonlinear Sciences - Adaptation and Self-Organizing Systems
Year: 2011
DOI identifier: 10.1063/1.3596697
OAI identifier: oai:arXiv.org:1103.0323
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