中文摘要：

基于Lyapunov稳定性理论和非线性动力学理论，构造出相应的非线性控制器，实现了三维混沌系统与四维超混沌系统之间异结构完全同步与反相同步控制，并对上述2类同步给出了严格的数学证明。以一个新型三维自治系统为例，引入状态反馈变量，构造了一个新的超混沌系统，研究了不同维数混沌系统之间的异结构完全同步与反相同步问题。最后，借助于Runge—Kutta算法进行数值仿真，通过对误差系统的误差进行分析，得到驱动系统和响应系统状态变量误差能在短时间内快速趋于零，表明理论推导的正确性和所提出方案的有效性。

英文摘要：

Based on the Lyapunov stability theory and nonlinear dynamic theory, a controller is designed, the con- trol of complete synchronization and anti - phase synchronization between 3 - dimensional and 4 - dimensional cha- otic systems with different structures is implemented, and the two kind of synchronization are respectively proved strictly in mathematics. In this paper, taking a new 3D autonomous system for example, hyper- chaotic system is achieved by introducing an additional state variable to the new 3D chaotic system, thus a complete synchronization and anti -phase synchronization between chaotic systems with different structures and dimensions are investigated. Finally, by the Runge - Kutta scheme numerical simulation and from the simulation analysis of the error system be- tween driving and coupled system, the graph of the errors can show that errors will become zero in short time, the numerical simulation shows the validity of the theoretical analysis and the effectiveness of the proposed method.