The Change Of The Kinetic Unit In The Transformation Of The Association And The Influence Of The Network Structure On The Singularity

The coupled nonlinear systems can show rich collective behaviors. The mechanism of collective behavior in coupled group is a basic problem in nonlinear kinetics study. In the globally coupled systems, such as, the Kuramoto phase oscillator model and Kaneko chaotic mapping model, many special dynamical behaviors are found. The system varies from completely chaotic synchronization to completely asynchronization, as the decrease of coupling strength. In the nearest neighbor coupled system, the rich dynamic characteristics are discovered, such as Solitons, and kinks.The chimera state in coupled nonlinear oscillator networks is an important discovery in recent years, which is the coexisted states of coherence state and incoherence state, appearing in many different kinds of oscillator networks with nonlocal coupling. The lyapunov exponent and analytical solution about the chimera state are studied. The dynamic mechanics of chimera state is thought to be associated with hemisphere sleep function of some animals.In this paper, we study the networks of coupled logistic map with nonlocal interaction. The main focus is to investigate the variation of the state of a single node with respect to the spatial correlation. We proposed a simulation method to record the mechanics of dynamical unit. By restricting the initial condition, one may find the bifurcation transitions of the individual nodes, including multiband chaotic state and multi-periodic state. Our records predicate a new chimera state in nonlocal coupling logistic maps. Based on the systematical analysis of the relation between the states of nodes and collective behavior, we find a new chimera state and also the agreement between the variation of state of single node and the nature measured by direction phase.In addition, we study the effect of network structure for chimera state. In nonlocal coupling networks, whether periodic boundary condition is adopted or not, the chimera state appears. Reconnecting the edges of nonlocal networks with a certain probability, the network changes from regular network to small-world network gradually, and finally becomes random network completely. The other chimera state arises in this process, but in the end, both of the two kinds of chimera states disappear when the network become completely random networks.