二维Ushiki离散系统的混沌控制研究  

The Study of Chaos Control of Two-dimensional Ushiki Discrete System

作　　者：付景超[1] 金立超 FU Jing-chao;JIN Li-chao(College of Science,Northeast Electric Power University,Jilin 132012,China)

机构地区：[1]东北电力大学理学院,吉林吉林132012

出　　处：《数学的实践与认识》2021年第24期193-202,共10页Mathematics in Practice and Theory

摘　　要：研究了二维Ushiki离散系统的混沌控制问题.首先分析了不动点的稳定性,通过绘制Lyapunov指数谱和波形图证实了混沌吸引子的存在;其次,通过分析分岔图和最大Lyapunov指数谱,获得了Ushiki离散系统的复杂动力学性质;最后,设计了两种不同的控制器,将混沌系统稳定到平衡点和周期轨道上,数值仿真验证了控制器的有效性.得出了混沌跟踪控制方法比Lyapunov指数配置方法具有更广泛的应用范围的结论.The chaos control problem of two-dimensional Ushiki discrete system is studied.Firstly,the stability of fixed point is analyzed,and the existence of chaotic attractor is confirmed by drawing Lyapunov exponent spectrum and waveform diagram.Secondly,by analyzing bifurcation diagram and maximum Lyapunov exponent spectrum,the complex dynamic properties of Ushiki discrete system are obtained.Finally,two different controllers are designed to stabilize the chaotic system on the equilibrium point and periodic orbit,the effectiveness of the controller is verified by numerical simulation.It is concluded that the chaos tracking control method has a wider application range than the Lyapunov exponential collocation method.

关 键 词：Ushiki离散系统 分岔 LYAPUNOV指数 混沌跟踪控制 Lyapunov指数分布 

分 类 号：O415.5[理学—理论物理] O231[理学—物理]