一个大Lyapunov指数四维超混沌系统分析及同步

Analysis and Synchronization of a Four-dimensional Hyperchaotic System with Large Lyapunov Exponent

在一个三维混沌系统的基础上构造了一个有大Lyapunov指数的四维超混沌系统,分析了该系统的耗散性和平衡点的稳定性。在所有系统参数中,改变某个参数而固定其余参数,依次计算和分析了系统各个参数的变化对系统Lyapunov指数谱的影响,从Lyapunov指数谱随各参数的变化判断系统作混沌运动和超混沌运动的参数变化区间。然后用相图研究了系统随系统参数变化时的运动规律。最后设计了一种线性反馈控制器实现了该超混沌系统的混沌同步,结果表明该方法正确有效。该系统在混沌和超混沌运动参数区间表现出的混沌和超混沌特性可以给基于混沌和超混沌理论的工程应用提供更多选择。所得结果为该超混沌系统在混沌保密通信中的应用提供了理论参考。

A four dimensional hyperchaotic system with a large Lyapunov exponent was constructed based on a three-dimensional chaotic system,and its dissipation and stability of the equilibrium point were analyzed.One parameter changed and other parameters fixed,the impact of each parameter change on the Lyapunov exponent spectrum of the system was calculated and analyzed sequentially.From the variation of Lyapunov exponent spectrum with each parameter,the parameter variation ranges of chaotic and hyperchaotic motion of the system were determined.Then,the phase diagram was used to study the motion law of the system with variation of system parameters.Finally,a linear feedback controller was designed to achieve chaos synchronization of the hyperchaotic system,and the results showed that the method was correct and effective.The chaotic and hyperchaotic characteristics of the system in the chaotic and hyperchaotic motion parameter ranges can provide more options for engineering applications based on chaotic and hyperchaotic theories.The obtained results provide a theoretical reference for the application of the hyperchaotic system in chaotic secure communication.