Adaptive generalized functional synchronization of chaotic systems with unknown parameters

A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R\"{o}ssler chaotic system and the four-dimensional Chen's hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.