Analysis of chaotic wandering of phase patterns in a two-dimensional coupled chaotic circuits network

Studies on spatio-temporal phenomena observed from coupled chaotic networks, namely coupled systems of many chaotic cells, are classified into two categories; namely discrete time systems and continuous time systems. For discrete time systems Kaneko’s coupled map lattice is the most interesting and well-studied system [l]. He discovered various nonlinear spatiotemporal chaotic phenomena such as clustering, Brownian motion of defect and so on. -41~0 -4ihara’s chaos neural network is the most important chaotic network from an engineering point of view [2]. His studv indicated new possibility of engineering applications of chaotic networks, namely dynamical search of patterns embedded in neural networks utilizing chaotic wandering. Further; application of chaos neural network to optimization problems is widely studied. However, for continuous time systems there have been few studies on spatial patterns observed after vanishing the effect of initial patterns. Therefore, in order to fill the gap between the studies of discrete-time mathematical abstract and studies of continuous-time real physical systems, it is important to investigate simple continuoustime coupled chaotic circuits networks generating clustering or pattern switching phenomenon. We have proposed a continuous-time coupled chaotic circuits network [3]-[6] and have reported generating spatial patterns, irregular self-switching phenomenon of spatial patterns, pattern control and so on. The important feature of our chaotic network is its couplmgstructure. Namely adjacent four chaotic circuits are coupled by one resistor. Because such a coupling exhibited quasi-synchronization with phase difference [7], various spatial patterns could be generated in the chaotic network. Therefore, the network would be a good model to make clear physical mechanism of spatio-temporal chaotic phenomena in continuoustime systems. However, chaotic wandering phenomena of phase patterns observed from a relatively larger size of the network has not been investigated. In this study, we investigate chaotic wandering phenomena of spatial patterns characterized bv phase differences in the coupled chaotic circuits network with 10x10 size. Snapshots of the Poincare map tell how switchings of phase states start and spread over the network. Further, we can show that an independent angular variables derived from higher-dimensional Poincare map can be effectively utilized in order to check the switching of phase states around coupling resistors.