Chaotic Griffiths Phase with Anomalous Lyapunov Spectra in Coupled Map Networks

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.

6 pages +2 pages Supplement (6 figues + 3 Supplement Figures)

References in corpus (5)

• Emergent complex neural dynamics
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Delays, connection topology, and synchronization of coupled chaotic maps
• Griffiths phases on complex networks
• Maximum Performance at Minimum Cost in Network Synchronization

Cited by in corpus (3)

• Criticality in Reservoir Computer of Coupled Phase Oscillators
• Stretched exponential dynamics of coupled logistic maps on a small-world network
• Association schemes perspective of microbubble cluster in ultrasonic fields