A robust method for classification of chimera states

TL;DR

This paper introduces a Fourier-based statistical classification method to reliably identify and distinguish chimera states in complex coupled oscillator systems, demonstrating robustness across various network configurations.

Contribution

A novel, automated framework combining Fourier analysis and statistical classification for systematic detection of chimera states in nonlinear dynamical systems.

Findings

Successfully classifies chimera states in a topological oscillator system

Demonstrates robustness to network topology variations

Provides a general tool for dynamical regime identification

Abstract

Chimera states are one of the most intriguing phenomena in nonlinear dynamics, characterized by the coexistence of coherent and incoherent behavior in systems of coupled identical oscillators. Despite extensive studies and numerous observations in different settings, the development of reliable and systematic methods to classify chimera states and distinguish them from other dynamical patterns remains a challenging task. Existing approaches are often limited in scope and lack robustness. In this work, we propose a method based on Fourier analysis combined with statistical classification to characterize chimera behavior. The method is applied to a system of topological signals coupled via the Dirac operator, where it successfully captures the rich dynamical regimes exhibited by the model. We demonstrate that the proposed approach is robust with respect to variations in network topology and system parameters. Beyond the specific model considered, the framework provides a general and automated tool for distinguishing different dynamical regimes in complex systems.