WAVE PROPAGATION, PATTERN FORMATION AND MEMORY EFFECTS IN LARGE ARRAYS OF INTERCONNECTED CHAOTIC CIRCUITS

Abstract

We investigate complex dynamic phenomena in arrays composed of interacting chaotic circuits. Such arrays can be thought of as a model of nonlinear phenomena in spatially extended (high-dimensional or infinite-dimensional) systems and active media with potential applications in brain function modelling and signal processing. In this paper we consider a particular structure of the network in which there exist locally double diffusive interactions between the cells. Such a double interaction can be considered as a paradigm and means for understanding very complex interactions existing in real systems where neighboring cells can communicate in various ways. We consider two basic cases where separate cells without coupling exhibit two different types of chaotic behavior. Depending on the connection structure, initial conditions imposed in the cells the array exhibits various kinds of spatially ordered chaotic waves. Patterns of behavior depending on the excitation of the array and the connection structure are studied in some detail. We present results of simulations showing cooperative phenomena. Depending on the connection structure between the cells and their initial states the array can show spatially ordered patterns of behavior. Such orderly spatial patterns resulting in arrays of chaotic elements are referred to as self-organization. We observed travelling target waves and chaotic wavefronts behaving like autowaves. This kind of autowave-like behavior in arrays of chaotic elements is to our knowledge described for the first time.