Chaotic behavior in diffusively coupled systems

TL;DR

This paper investigates how diffusively coupled nonlinear systems can exhibit chaotic oscillations, providing general conditions and a bifurcation theory framework for such emergent complex behavior.

Contribution

It introduces the concept of versatile network configurations and develops a bifurcation theory for diffusively coupled networks to explain chaos emergence.

Findings

Chaotic behavior can be induced in networks with homogeneous diffusive coupling.

The paper establishes conditions for chaos based on local bifurcation theory.

Versatile networks allow for flexible bifurcation properties.

Abstract

We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an arbitrary network configuration, general conditions for the existence of the diffusive coupling of a homogeneous strength which makes the network dynamics chaotic. The method is based on the theory of local bifurcations we develop for diffusively coupled networks. We, in particular, introduce the class of the so-called versatile network configurations and prove that the Taylor coefficients of the reduction to the center manifold for any versatile network can take any given value.