The Stability of Hybrid Liu Chaotic System with a Sort of Oscillating Parameters under Impulsive Control

The control of chaotic synchronization have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system by using the information of the chaotic system. In this paper we propose a hybrid Liu chaotic synchronization control scheme which contains both continuous chaotic system with a sort of oscillating parameters and discrete chaotic system. By theory of impulsive differential equations, we proved a theorem that two continuous Liu chaotic systems can get synchronized without control signal transmitting which has reduced the risk of the security.