In this chapter, four coupled chaotic circuits that can generate four-phase quasi-synchronization of chaos are proposed. By tuning the coupling parameter, chaotic wandering over the phase states characterized by the four-phase synchronization occurs. In order to analyze chaotic wandering, dependent variables corresponding to phases of solutions in sub-circuits are introduced. Combining the variables with hysteresis decision of the phase states enables statistical analysis of chaotic wandering.

4.1 Introduction

Spatiotemporal phenomena observed in coupled chaotic networks, namely coupled systems of many chaotic cells, have attracted many researchers' attention. The studies on coupled chaotic networks are classified into two categories: discrete-time systems and continuous-time systems. For discrete-time mathematical models, there have been numerous excellent results. Kaneko's coupled map lattice is the most interesting and well-studied system ^[1]. He discovered various nonlinear spatiotemporal chaotic phenomena such as clustering, Brownian motion of defects, and so on. Also, Aihara's chaotic neural network is the most important chaotic network from an engineering point of view ^[2]. His study indicated a new possibility for engineering applications of chaotic networks, namely dynamical search of patterns embedded in neural networks utilizing chaotic wandering. Furthermore, the application of chaotic neural networks to optimization problems is widely studied ( ^[3] and references therein). On the other hand, for continuous-time systems, several results on arrays of Chua's circuits have been reported (e.g., some papers in ^[4]). However, the main subject of many studies...