Generalized chaos synchronization theorem for array differential equations with application

This paper establishes one new constructive generalized (chaos) synchronization (GS) theorems for coupled array ordinary differential equation systems (ADESs). The theorems provide general representations of GS ADES. Based on the theorem, one can design GS driven ADESs via driving chaotic ADESs and continuously differentiable transformations. As an applications, a Lorenz's cellular neural network (CNN) is introduced. Using the GS theorems and the new CNN constructs a coupled GS ADES. The hyper chaotic GS phenomena of the GS ADES have been simulated. The numerical simulation results display complex behaviors of the GS ADES. It may be expected that our theorem provide new tools for understanding GS and study ADESs.