Basins of Attraction for Chimera States

TL;DR

This paper investigates the complex structure of basins of attraction for chimera states in coupled oscillators, combining analytical and numerical methods to understand their formation and potential control strategies.

Contribution

It provides a detailed analysis of the basin structures for chimera states in a two-population oscillator system, revealing their complex twisting geometry.

Findings

Basins form a complex twisting structure in phase space.

Perturbative analysis and simulations effectively evaluate asymptotic states.

Understanding basin structures may enable control of chimera patterns.

Abstract

Chimera states---curious symmetry-broken states in systems of identical coupled oscillators---typically occur only for certain initial conditions. Here we analyze their basins of attraction in a simple system comprised of two populations. Using perturbative analysis and numerical simulation we evaluate asymptotic states and associated destination maps, and demonstrate that basins form a complex twisting structure in phase space. Understanding the basins' precise nature may help in the development of control methods to switch between chimera patterns, with possible technological and neural system applications.