Collective chaos induced by structures of complex networks

Mapping a complex network of N   coupled identical oscillators to a quantum system, the nearest neighbor level spacing (NNLS) distribution is used to identify collective chaos in the corresponding classical dynamics on the complex network. The classical dynamics on an Erdos–Renyi network with the wiring probability pER⩽1/NpER⩽1/N is in the state of collective order, while that on an Erdos–Renyi network with pER>1/NpER>1/N in the state of collective chaos. The dynamics on a WS Small-world complex network evolves from collective order to collective chaos rapidly in the region of the rewiring probability pr∈[0.0,0.1]pr∈[0.0,0.1], and then keeps chaotic up to pr=1.0pr=1.0. The dynamics on a Growing Random Network (GRN) is in a special state deviates from order significantly in a way opposite to that on WS small-world networks. Each network can be measured by a couple values of two parameters (β,η)(β,η).