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∼2(β+1) is uncovered, which is universal independent of parameters and among random networks.