Bifurcation and chaos in discrete-time cellular neural networks

Abstract

This paper studies bifurcation and chaos in discrete-time cellular neural networks (DTCNN), whose cells, similar to that in continuous-time CNN's, are locally coupled and whose output equations are logistic equations. The chaotic behavior of two types of DTCNN arrays, bounded and unbounded, is discussed respectively. While there is similarity between chaos of DTCNN's and that of globally coupled systems (Kaneko, 1990) DTCNN's differ from the latter in their bifurcation and statistical features due to their special locally coupled structure. Initial study on bifurcation and chaos in two-dimensional DTCNN arrays are presented in this paper with some interesting theoretical and practical problems proposed for our future research on this subject.<>