Transition from spatial coherence to incoherence in coupled chaotic systems

TL;DR

This paper explores how coupled chaotic systems transition from spatially coherent patterns to incoherent chaos, analyzing the influence of coupling parameters across different models.

Contribution

It introduces a unified analysis of the coherence-incoherence transition in coupled chaotic systems, supported by theoretical derivations and numerical simulations across various models.

Findings

Identification of a critical coupling strength for transition

Scaling relation for coherent profile sizes

Universality across different chaotic models

Abstract

We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we find characteristic spatial patterns such as wave-like profiles and study the transition from coherence to incoherence leading to spatial chaos. We analyze the origin of this transition based on numerical simulations and support the results by theoretical derivations identifying a critical coupling strength and a scaling relation of the coherent profiles. To demonstrate the universality of our findings we consider time-discrete as well as time-continuous chaotic models realized as logistic map and R\"ossler or Lorenz system, respectively. Thereby we establish the coherence-incoherence transition in networks of coupled identical oscillators.