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arXiv · 1103.0323

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

Wai Shing Lee·Juan G. Restrepo·Edward Ott·Thomas M. Antonsen
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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.

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Wai Shing Lee, Juan G. Restrepo, Edward Ott, Thomas M. Antonsen. 2011-03-02. Dynamics and Pattern Formation in Large Systems of Spatially-Coupled Oscillators with Finite Response Times. https://doi.org/10.1063/1.3596697

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