Generalized reduced-order synchronization of chaotic system based on fast slide mode

A new kind of generalized reduced-order synchronization of different chaoticsystems is proposed in this paper. It is shown that dynamical evolution ofthird-order oscillator can be synchronized with the canonical projection ofa fourth-order chaotic system generated through nonsingular statestransformation from a cell neural net chaotic system. In this sense, it issaid that generalized synchronization is achieved in reduced-order. Thesynchronization discussed here expands the scope of reduced-ordersynchronization studied in relevant literatures. In this way, we can achievegeneralized reduced-order synchronization between many famous chaoticsystems such as the second-order D"{u}ffing system and the third-orderLorenz system by designing a fast slide mode controller. Simulation resultsare provided to verify the operation of the designed synchronization.