Imperfect synchronized states and chimera states in two interacting populations of nonlocally coupled Stuart-Landau oscillators

TL;DR

This paper explores the emergence and stability of imperfect synchronized and chimera states in two interacting populations of nonlocally coupled Stuart-Landau oscillators, revealing how parameters influence these complex dynamics.

Contribution

It introduces the concept of imperfect synchronized states and mixed chimera states in coupled oscillator populations, highlighting the effects of nonisochronicity and frequency mismatch.

Findings

Imperfect synchronized states occur with small nonisochronicity.

Mixed imperfect synchronized states emerge at higher nonisochronicity.

Chimera states coexist with synchronized and desynchronized oscillations.

Abstract

We investigate the emergence of different kinds of imperfect synchronized states and chimera states in two interacting populations of nonlocally coupled Stuart-Landau oscillators. We find that the complete synchronization in population-I and existence of solitary oscillators which escape from the synchronized group in population-II lead to imperfect synchronized states for sufficiently small values of nonisochronicity parameter. Interestingly, on increasing the strength of this parameter further there occurs an onset of mixed imperfect synchronized states where the solitary oscillators occur from both the populations. Synchronized oscillators from both the populations are locked to a common average frequency. In both the cases of imperfect synchronized states synchronized oscillators exhibit periodic motion while the solitary oscillators are quasi-periodic in nature. In this region, for spatially prepared initial conditions, we can observe the mixed chimera states where the coexistence of synchronized and desynchronized oscillations occur from both the populations. On the other hand, imperfect synchronized states are not always stable, and they can drift aperiodically due to instability caused by an increase of nonisochronicity parameter. We observe that these states are robust to the introduction of frequency mismatch between the two populations.