A GENERALIZED SYNCHRONIZATION THEOREM FOR AN ARRAY OF DIFFERENTIAL EQUATIONS WITH APPLICATION TO SECURE COMMUNICATION

This paper first presents a theorem for constructing a unidirectionally coupled array of differential equations (ADE) such that a driving system and a driven system achieve generalized synchronization (GS) via a set of invertible C 1 -diffeomorphism transformations. Secondly, a new secure communication scheme for digital image transformation is developed based on the theorem. Finally, a Chua's ADE with GS property is introduced, based on a prototype introduced by Chua as a two-dimensional dual-layer two-dimensional reaction–diffusion cellular neural network (CNN), and is applied to construct a secure image communication scheme.