Complex behavior in chains of nonlinear oscillators

TL;DR

This paper identifies conditions under which chains of excitable nonlinear oscillators exhibit complex spatio-temporal patterns due to local interactions and balanced excitation-inhibition, highlighting high-dimensional bifurcations.

Contribution

It provides theoretical conditions for complex behavior in one-dimensional oscillator chains with local interactions and balanced excitation and inhibition.

Findings

Complex behavior arises in networks with balanced local interactions.

High-dimensional bifurcations involve exponentially many equilibria.

Balanced excitation and inhibition are sufficient for emergent complexity.

Abstract

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions are sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.