线性反馈控制新的4维超混沌系统同步

Chaotic Synchronization for a New Four-dimensional Hyperchaos System Using Linear Feedback

为了改善基于混沌同步保密通讯系统的安全性能,在3维Lü系统的基础上增加1维状态,构建了一个新的简单的4维超混沌系统。简要地分析了该系统平衡点的性质、系统的分岔图、超混沌吸引子的相图、Lyapunov指数和Lyapunov维数等特性,并设计了一种实现4维超混沌系统的实际电路。利用线性反馈控制方法实现了该超混沌系统的混沌同步,根据系统的Lyapunov稳定性理论,得到了超混沌系统达到混沌同步时反馈控制增益的取值范围。数值实验的结果表明,该超混沌系统演化过程丰富且能用线性反馈控制方法实现混沌同步。

In order to improve the security of secure communication systems based on chaos synchronization, a new four-dimensional hyperchaos system was built by adding an additional state into the three-order Lü system. Some of its basic dynamical properties were studied briefly, such as the feature of equilibrium, the bifurcation diagram, the hyperchaos attractor, Lyapunov exponent and fractal dimension. An electronic circuit was designed to realize the four-dimensional hyperchaos system. A method of chaos synchronization between the four-dimensional hyperchaos system and its duplicate system using linear feedback control was proposed. Based on the Lyapunov stability theory, the range of feedback gain was derived. Computer simulation showed that the hyperchaos system has variety of states and chaos synchronization can be realized using linear feedback control.