Chaotic Griffiths Phase with Anomalous Lyapunov Spectra in Coupled Map Networks

TL;DR

This paper investigates the complex dynamics of coupled chaotic oscillators on networks, revealing a universal scaling relation between cluster size distribution and Lyapunov spectra that indicates a chaotic Griffiths phase.

Contribution

It uncovers a universal scaling relation between cluster size distribution and Lyapunov spectra in coupled map networks, indicating a chaotic Griffiths phase.

Findings

Cluster size distribution follows a power law with a parameter-dependent exponent.

Lyapunov spectra scale anomalously with system size, characterized by an exponent β.

A universal relation $ ext{α} ext{~} 2(eta +1)$ links the two exponents across parameters.

Abstract

Dynamics of coupled chaotic oscillators on a network are studied using coupled maps. Within a broad range of parameter values representing the coupling strength or the degree of elements, the system repeats formation and split of coherent clusters. The distribution of the cluster size follows a power law with the exponent $\alpha$, which changes with the parameter values. The number of positive Lyapunov exponents and their spectra are scaled anomalously with the power of the system size with the exponent $\beta$, which also changes with the parameters. The scaling relation $\alpha \sim 2(\beta +1)$ is uncovered, which seems to be universal independent of parameters and networks.