Loss of coherence in dynamical networks: spatial chaos and chimera states

TL;DR

This paper investigates how spatial coherence breaks down in networks of coupled oscillators, revealing a bifurcation scenario with intermediate states during the transition from coherence to incoherence.

Contribution

It introduces a systematic analysis of the coherence-incoherence transition in nonlocally coupled oscillators, highlighting the emergence of intermediate partially coherent states.

Findings

Identification of a bifurcation scenario for coherence loss

Discovery of narrow incoherent layers preceding full incoherence

Observation of intermediate partially coherent states during transition

Abstract

We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous R\"ossler systems reveal that intermediate, partially coherent states represent characteristic spatio-temporal patterns at the transition from coherence to incoherence.