Chaotic Griffiths Phase with Anomalous Lyapunov Spectra in Coupled Map Networks

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 $α$, 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 $β$, which also changes with the parameters. The scaling relation $α\sim 2(β+1)$ is uncovered, which seems to be universal independent of parameters and networks.

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