超混沌耦合发电机系统的混沌同步及其电路实现

Chaotic synchronization of hyper-chaotic coupled dynamos system and its circuit implementation

在三维耦合发电机系统的基础上增加一维状态,构建了一个新的四维超混沌耦合发电机系统,简要分析了该系统的平衡点、吸引子的相图、Lyapunov指数和Lyapunov维数等特性,设计了相应的电子电路,实验结果进一步证实了该系统是一个新的超混沌系统,不同于原有的三维耦合发电机系统;基于Lyapunov稳定性理论,设计了非线性同步控制器,从理论上构建了两种同步误差系统的Lyapunov函数,证明了新的超混沌系统的自同步以及与超混沌Lorenz系统的异结构同步,最后通过数值模拟验证了所提出方案的有效性.

The four-dimensional hyper-chaotic system is built by adding an additional state to the threeorder coupled dynamos system. Some of its basic dynamical properties are studied briefly, such as the feature of equilibrium, the hyper-chaotic attractor, Lyapunov exponent and fractal dimension, and an analog electronic circuit is designed to verify the new system. The experiment results show that the system is a new hyper-chaotic system. Moreover, it is different from three-order coupled dynamos system; Based on Lyapunov theory, a nonlinear controller is designed to synchronize two identical systems and two different chaotic systems. Two methods for improving the Lyapunov function of error dynamics of synchronization are presented. The methods remove the limitation occasioned by the Lyapunov function having only one form. Chaos synchronization of two identical hyper-chaotic coupled dynamos systems and two different hyper-chaotic systems （the hyper-chaotic coupled dynamos system and the hyper-chaotic Lorenz system） have been proved theoretically. Numerical simulations show the effectiveness of the proposed method.