Strong and weak chaos in nonlinear networks with time-delayed couplings

TL;DR

This paper explores how chaos manifests in nonlinear networks with time delays, distinguishing between strong and weak chaos based on Lyapunov exponents, and examines their impact on synchronization stability through simulations and experiments.

Contribution

It introduces the concepts of strong and weak chaos in delayed networks and links these to synchronization stability criteria, supported by simulations and electronic circuit experiments.

Findings

Transitions between weak and strong chaos observed with increasing coupling strength

Strong chaos correlates with unstable synchronization

Weak chaos allows for stable synchronization

Abstract

We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for large delay times, and relate this to the condition for stable or unstable chaotic synchronization, respectively. In simulations of laser models and experiments with electronic circuits, we identify transitions from weak to strong and back to weak chaos upon monotonically increasing the coupling strength.