# Lyapunov Analysis of Chimera States in Globally Coupled Stuart-Landau oscillators

## TL;DR

This paper uses Lyapunov analysis to explore the collective dynamics of chimera states in globally coupled Stuart-Landau oscillators, revealing differences in their Lyapunov spectra and modes depending on the type of global coupling.

## Contribution

It introduces a Lyapunov-based approach to distinguish and analyze chimera states in different globally coupled oscillator systems, highlighting qualitative differences in their collective modes.

## Key findings

- Lyapunov spectra split into distinct groups with system size
- Lyapunov dimension scales extensively with system size
- Different coupling types exhibit distinct collective Lyapunov modes

## Abstract

Oscillatory systems with long-range or global coupling offer promising insight into the interplay between high-dimensional (or microscopic) chaotic motion and collective interaction patterns. Within this paper, we use Lyapunov analysis to investigate whether chimera states in globally coupled Stuart-Landau (SL) oscillators exhibit collective degrees of freedom. We compare two types of chimera states, which emerge in SL ensembles with linear and nonlinear global coupling, respectively, the latter introducing a constraint that conserves the oscillation of the mean. Lyapunov spectra reveal that for both chimera states the Lyapunov exponents split into different groups with different convergence properties in the limit of large system size. Furthermore, in both cases the Lyapunov dimension is found to scale extensively and the localization properties of covariant Lypunov vectors manifest the presence of collective Lyapunov modes. Here, however, we find qualitative differences between the two types of chimera states: Whereas the ones in the system under nonlinear global coupling exhibit only slow collective modes corresponding to Lyapunov exponents equal or close to zero, those which experience the linear mean-field coupling exhibit also faster collective modes associated with Lyapunov exponents with large positive or negative values.