Effect of asymmetry parameter on the dynamical states of nonlocally coupled nonlinear oscillators

TL;DR

This paper investigates how the asymmetry parameter in nonlocal rotational matrix coupling influences the emergence of chimera states in ensembles of identical nonlinear oscillators, demonstrating robustness across various systems.

Contribution

It introduces the role of the asymmetry parameter in inducing and controlling chimera states in nonlocally coupled nonlinear oscillators, extending understanding beyond symmetric coupling.

Findings

Chimera states can be induced over a wide range of the asymmetry parameter.

The asymmetry parameter robustly induces chimeras in different dynamical systems.

Distinction between frequency and amplitude chimeras is established.

Abstract

We show that coexisting domains of coherent and incoherent oscillations can be induced in an ensemble of any identical nonlinear dynamical systems using the nonlocal rotational matrix coupling with an asymmetry parameter. Further, chimera is shown to emerge in a wide range of the asymmetry parameter in contrast to near $\frac{\pi}{2}$ values of it employed in the earlier works. We have also corroborated our results using the strength of incoherence in the frequency domain ($S_{\omega}$) and in the amplitude domain ($S$) thereby distinguishing the frequency and amplitude chimeras. The robust nature of the asymmetry parameter in inducing chimeras in any generic dynamical system is established using ensembles of identical R\"ossler oscillators, Lorenz systems, and Hindmarsh-Rose (HR) neurons in their chaotic regimes.