GENERALIZED SYNCHRONIZATION IN AN ARRAY OF NONLINEAR DYNAMIC SYSTEMS WITH APPLICATIONS TO CHAOTIC CNN

This paper establishes some generalized synchronization (GS) theorems for a coupled discrete array of difference systems (CDADS) and a coupled continuous array of differential systems (CCADS). These constructive theorems provide general representations of GS in CDADS and CCADS. Based on these theorems, one can design GS-driven CDADS and CCADS via appropriate (invertible) transformations. As applications, the results are applied to autonomous and nonautonomous coupled Chen cellular neural network (CNN) CDADS and CCADS, discrete bidirectional Lorenz CNN CDADS, nonautonomous bidirectional Chua CNN CCADS, and nonautonomously bidirectional Chen CNN CDADS and CCADS, respectively. Extensive numerical simulations show their complex dynamic behaviors. These theorems provide new means for understanding the GS phenomena of complex discrete and continuously differentiable networks.