A Generalized Chaos Synchronization Theorem for Array Differential Equations with Application

A constructive generalized chaos synchronization (GS) theorem for unidirectionally coupled array ordinary differential equation systems (ADESs) is presented. Based on the theorem, one can design a GS driven ADES via a driving chaotic ADES and a C¹ diffeomorphism. As an application, a Duffing cellular neural network (CNN) with four state variables is introduced. Using the GS theorem and the Duffing CNN constructs coupled GS ADESs with 3087 cells. The hyper chaotic GS phenomena of the GS ADESs have been simulated. The numerical simulation results display complex behaviors of the GS ADESs.