Abstract
Based on the Lyapunov stability theory, an improved Lyapunov function scheme is used to understand the complete synchronization of hyperchaotic systems by imposing pulse linear coupling on the response system. According to this scheme, the controller begins to control the response system in a period when the output error variables are increasing; otherwise, the controller turns off. The distribution of conditional Lyapunov exponent versus coupling intensity, and the synchronization cost (averaged power consumption of controller) is calculated, respectively. By designing an exponential type of Lyapunov function, it is found that complete synchronization could be realized between two Chen hyperchaotic systems and two 4-dimensional LC hyperchaotic systems. Our numerical results are consistent with the previous theoretical discussion.
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