Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

TL;DR

This paper introduces a new type of chimera state in an ensemble of identical oscillators influenced by a common environment, revealing complex coexistence of synchronized and asynchronous domains.

Contribution

It demonstrates the existence of a novel chimera state driven by phase-flip bifurcation in nonlocally coupled oscillators influenced by a dynamic environment.

Findings

Discovery of a new chimera state with out-of-phase synchronized domains

Identification of various collective behaviors like clusters and solitary states

Robustness confirmed in R"ossler and Stuart-Landau oscillator ensembles

Abstract

A complex collective emerging behavior characterized by coexisting coherent and incoherent do- mains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators driven by a common dynamic environment. The latter facilitates the onset of phase-flip bifurcation/transitions among the coupled oscillators of the ensemble, while the nonlocal coupling induces a partial asynchronization among the out-of-phase synchronized oscillators at this onset. This leads to the manifestation of coexisting out-of-phase synchronized coherent domains interspersed by asynchronous incoherent domains elucidating the existence of a different type of chimera state. In addition to this, a rich variety of other collective behaviors such as clusters with phase-flip transition, conventional chimera, solitary state and com- plete synchronized state which have been reported using different coupling architectures are found to be induced by the employed couplings for appropriate coupling strengths. The robustness of the resulting dynamics is demonstrated in ensembles of two paradigmatic models, namely R\"ossler oscillators and Stuart-Landau oscillators.