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

TL;DR

This paper models large systems of spatially-coupled oscillators with varying response times, revealing complex spatio-temporal patterns like spirals, chimeras, and propagating fronts through a macroscopic PDE approach.

Contribution

It introduces a macroscopic PDE framework for analyzing oscillators with finite response times, extending previous models to include diverse natural frequencies and response delays.

Findings

Finite response times induce rich spatio-temporal patterns.

Patterns include propagating fronts, spots, and spiral waves.

Interactions and evolution of patterns are characterized.

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.