一个大Lyapunov指数四维超混沌系统及其控制和同步  

Study on control and synchronization of a four-dimensional hyperchaotic system withlarge Lyapunov exponent

作　　者：杨旦旦 邓林 YANG Dandan;DENG Lin(Department of Civil Engineering,Sichuan College of Architectural Technology,Deyang 618000,China)

机构地区：[1]四川建筑职业技术学院土木工程系,四川德阳618000

出　　处：《佛山科学技术学院学报（自然科学版）》2023年第4期63-71,共9页Journal of Foshan University(Natural Science Edition)

摘　　要：构造了一个新的具有大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。改变一个系统参数而固定其他系统参数,计算和分析了系统各个参数的变化对系统的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。用相图研究了系统随系统参数变化时的运动规律。设计了一种线性反馈控制器将该超混沌系统控制到平衡点。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。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理论和超混沌理论的工程应用提供选择。计算及分析方法具有一般性,对于其他超混沌系统的动力学分析、控制和同步具有借鉴意义。A new four-dimensional hyperchaotic system with large Lyapunov exponent was constructed.The dissipation of the system and the stability of the equilibrium point were analyzed.By changing one system parameter while fixing other system parameters,the influence of the change of each system parameter on the Lyapunov exponent spectrum of the system was calculated and analyzed,and the parameter change ranges of the chaotic motion and hyperchaotic motion of the system were judged from the change of Lyapunov exponent spectrum with each parameter.Then the phase diagram was used to study the motion law of the system with the change of system parameters.The hyperchaotic system was controlled to the equilibrium point by linear feedback control method.The hyperchaotic system was synchronized by linear feedback control method.The chaotic and hyperchaotic characteristics of the system in chaotic and hyperchaotic motion parameter ranges can provide a choice for engineering applications based on chaos and hyperchaos theory.The calculation and analysis methods are universal and have reference significance for the dynamic analysis and control of other hyperchaotic systems.

关 键 词：超混沌系统 LYAPUNOV指数 参数区间 吸引子 超混沌控制 超混沌同步 

分 类 号：O415.5[理学—理论物理]