中文摘要：

基于李亚普诺夫稳定性理论，构造了指数型的李亚普诺夫函数，以四变量的Chen超混沌系统为例，解析地证明了线性耦合实现同步的可靠性．进一步研究了非线性耦合对线性耦合同步的调制作用．基于无量纲化的动力学方程定义一个统计函数来估算控制器的消耗功率，确定了线性耦合与非线性耦合实现同步对应的参数范围，数值计算结果验证了理论结果的可靠性．

英文摘要：

Based on the Lyapunov stability theory, the Lyapunov function in the form of exponential type is constructed. The four-variable Chen hyperchaotic model is investigated as an example. The reliability of a linear coupling-inudced synchronization of hyperchaotic system is proofed analytically. Furthermore, the modulation effect of nonlinear coupling on the synchronization induced by linear cou- pling is investigated. A statictical function is defined to evaulate the power consumption of controller according to the dimensionaless dynamical equations, the appropriate parameter region for synchronization due to the joint action of linear and nonlinear coupling, and the extensive numerical results confirm the correctress of the theoretical predication.