A General Criterion for Unidirectionally Coupled Generalized Chaotic Synchronization with a Desired Manifold

In this paper, a general criterion for unidirectionally coupled generalized chaotic synchronization between the response system and the original chaotic system in the form of a desired manifold is presented. The expression of the response system constructed with linear error feedback is given, and the validity of the criterion is proved based on the Lyapunov stability theory. Two numerical examples are used to construct unidirectional coupled chaotic systems in the form of different types of manifolds. Numerical simulation is carried out to verify the feasibility of the construction method and the criterion.