# Occurrence and stability of chimera states in multivariable coupled flows

## TL;DR

This paper explores the creation and stability of chimera states in multivariable coupled oscillators, demonstrating how tuning bifurcation parameters can produce stable coexistence of synchronized and desynchronized groups.

## Contribution

It introduces a novel scheme for generating and analyzing chimera states in multivariable systems, including stability assessment using MSF and basin structure analysis.

## Key findings

- Chimera states can be created by tuning bifurcation parameters in coupled oscillators.
- The stability of chimera states is verified using the Master Stability Function.
- Basins of attraction for chimera states are riddled or intertwined.

## Abstract

Study of collective phenomenon in populations of coupled oscillators are a subject of intense exploration in physical, biological, neuronal and social systems. Here we propose a scheme for the creation of chimera states, namely the coexistence of distinct dynamical behaviors in an ensemble of multivariable coupled oscillatory systems and a novel scheme to study their stability. We target bifurcation parameters that can be tuned such that out of the two coupling parameters one pushes the system to synchrony while the other one takes it to the desynchronized state. The competition between these states result in a situation that a certain fraction of oscillators are synchronized while others are desynchronized thereby producing a mixed chimera state. Further changes in couplings can result in the desired form of the state which could be completely synchronized or desynchronized. Using the model example of coupled R\"ossler systems we show that their basin of attraction are either riddled or intertwined. We use Strength of incoherence and Master Stability function (MSF) as the order parameters to verify the stability of chimera states. MSF for different attractors are found to possess both negative and positive values indicating the coexistence of stable synchronized dynamics with desynchronized state.