混沌系统的动力学分析及能量反馈控制
Dynamical Analysis and Energy Feedback Control of Chaotic Systems
DOI: 10.12677/AAM.2022.1110773, PDF,   
作者: 王文静*, 于欢欢, 路正玉：广东理工学院基础教学部，广东 肇庆
关键词: 混沌系统；Hamilton能量；能量控制；Chaotic System； Hamilton Energy； Energy Control
摘要: 随着对混沌现象研究的深入，混沌系统的动力学行为变化及对混沌状态的控制研究已成为研究混沌的重要任务。本文构造了一个具有多个平衡点的混沌系统，在理论分析和数值仿真下，详细分析了系统的基本动力学特性，并通过Routh-Hurwitz定理分析了平衡点的稳定性以及作出了系统的分岔图。同时在计算了系统的Hamilton能量后，通过增加一个与Hamilton能量相关的新变量来改进动力学系统，并通过调整能量的反馈增益找到目标轨道。结果表明，为Hamilton能量设置适当的正反馈增益可以抑制混沌。
Abstract: With the deepening of the study of chaos, the dynamic behavior changes of chaotic systems and the control of chaotic state have become an important task in the study of chaos. In this paper, a class of chaotic systems with multiple equilibrium points is constructed. Based on theoretical analysis and numerical simulation, the basic dynamic characteristics of the system are analyzed in detail, and the stability of the equilibrium point is analyzed by Routh-Hurwitz theorem and bifurcation dia-gram of the system is obtained. After calculating the Hamiltonian energy of the system, a new varia-ble related to the Hamiltonian energy was added to improve the dynamics system, and the target orbit was found by adjusting the feedback gain of the energy. The results show that chaos can be suppressed by proper positive feedback gain for Hamiltonian energy.
文章引用：王文静, 于欢欢, 路正玉. 混沌系统的动力学分析及能量反馈控制[J]. 应用数学进展, 2022, 11(10): 7284-7290. https://doi.org/10.12677/AAM.2022.1110773

参考文献

[1] Christiansen, P.L., Sorensen, M.P. and Scott, A.C. (2000) Nonlinear Science at the Dawn of the 21st Century. Springer, Berlin, 323-337. [Google Scholar] [CrossRef] 
[2] Ahmad, W.M. (2005) Generation and Control of Multi-Scroll Chaotic Attractors in Fractional Order Systems. Chaos, Solitons and Fractals, 25, 727-735. [Google Scholar] [CrossRef] 
[3] 刘明华, 禹思敏. 多涡卷高阶广义Jerk电路[J]. 物理学报, 2006, 55(11): 5707-5713.
[4] Yalcin, M.E. (2007) Multi-Scroll and Hypercube Attractors from a General Jerk Circuit Using Josephson Junctions. Chaos, Solitons and Fractals, 34, 1659-1666. [Google Scholar] [CrossRef] 
[5] 王震, 毛鹏伟. 一类三维混沌系统的分叉及稳定性分析[J]. 动力学与控制学报, 2008, 6(1): 16-21.
[6] Sharma, P.R., Shrimali, M.D., Prasad, A., Kuznetsov, N.V. and Leonov, G.A. (2015) Control of Multistability in Hidden Attractors. European Physical Journal Special Topics, 224, 1485-1491. [Google Scholar] [CrossRef] 
[7] Feng, Y. and Wei, Z. (2015) Delayed Feedback Control and Bi-furcation Analysis of the Generalized Sprott B System with Hidden Attractors. European Physical Journal Special Top-ics, 224, 1619-1636. [Google Scholar] [CrossRef] 
[8] Vaidyanathan, S. (2017) A Memristor-Based Hyperchaotic Sys-tem with Hidden Attractor and Its Sliding Mode Control. Studies in Computational Intelligence, 709, 343-369. [Google Scholar] [CrossRef] 
[9] Wu, F.Q., Wang, C.N., Jin, W.Y., et al. (2017) Dynamical Responses in a New Neuron Model Subjected to Electromagnetic Induction and Phase Noise. Physica A: Statistical Me-chanics and Its Applications, 469, 81-88. [Google Scholar] [CrossRef] 
[10] 王春妮, 王亚, 马军. 基于亥姆霍兹定理计算动力学系统的哈密顿能量函数[J]. 物理学报, 2016, 65(24): 1-6.

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