Generalized synchronization of two bidirectionally coupled discrete dynamical systems

Based on the modified system approach the generalized synchronization (GS) in two bidirectionally coupled discrete dynamical systems is classified into several types, and under some conditions, the existence, Lipschitz smoothness and Hölder continuity of two kinds of GS therein are derived and theoretically proved. In addition, numerical simulations validate the present theory.

► The main results of V. Afraimovich (2001) are generalized to two bidirectionally coupled discrete systems.
► The existence of the first Hölder continuous GS manifold is proved under the weaker condition than V. Afraimovich’s.
► We theoretically prove the existence and properties of two kinds of GS in two bidirectionally coupled discrete systems.