Diffusion-induced instability and chaos in random oscillator networks

TL;DR

This paper explores how diffusively coupled oscillators on random networks can become unstable and exhibit complex behaviors like chaos, partial amplitude death, and clustering, with a theoretical framework and numerical evidence.

Contribution

It introduces a network-based complex Ginzburg-Landau model to analyze diffusion-induced instabilities and their resulting complex dynamics in random oscillator networks.

Findings

Uniform oscillations can become unstable due to diffusional coupling.

Numerical simulations show emergence of chaos, clustering, and partial amplitude death.

A mean-field theory explains the nonlinear dynamical regimes.

Abstract

We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform oscillations can be linearly unstable with respect to spontaneous phase modulations due to diffusional coupling - the effect corresponding to the Benjamin-Feir instability in continuous media. Numerical investigations under this instability in random scale-free networks reveal a wealth of complex dynamical regimes, including partial amplitude death, clustering, and chaos. A dynamic mean-field theory explaining different kinds of nonlinear dynamics is constructed.