一个三元非线性二次项分数阶混沌系统的研究和控制
首发时间:2020-05-29
摘要:随着分数阶微积分理论的不断完善和发展,分数阶混沌系统的研究逐渐成熟起来,本文构造了一个具有三个非线性二次项的新分数阶混沌系统,通过改变其阶数对其混沌子相图进行了研究。通过特征方程的方法对其平衡点稳定性初步的研究,发现在阶数都小于0.797的情况下系统的非零点平衡点都将具有稳定性,同时改变系统的单参数研究了参数变化对系统所产生的影响,发现对于一次项的参数来说,参数的改变对系统的运动状态改变很大。通过Laplace变换对其混沌实现了控制,并且发现控制器常数越大的时候控制效果越好,基于现有的李雅普诺夫理论,实现了该系统的自适应同步和参数辨识,并通过数值仿真和对相图的研究,对该系统进行了更加深入的了解。?????
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Research and control of a ternary nonlinear quadratic fractional-order chaotic system
Abstract:With the continuous improvement and development of fractional-order calculus theory, the research of fractional-order chaotic systems has gradually matured. In this paper, a new fractional-order chaotic system with three nonlinear quadratic terms is constructed, and the subphase diagram was studied by changing its order. A preliminary study on the stability of its equilibrium point through the method of characteristic equations shows that the non-zero equilibrium point of the system will be stable when the order is less than 0.797. At the same time, the single parameter of the system is changed to study its effect. As a result, it is found that for the parameters of the primary term, the change of the parameters greatly changes the motion state of the system. The chaos is controlled by Laplace transform, and it is found that the greater the controller constant is, the better the control effect is. Based on the existing Lyapunov theory, adaptive synchronization and parameter identification of the system are realized. Through numerical simulation and The research on the phase diagram has made a deeper understanding of the system..
Keywords: Automation system theory, Fractional calculus,adaptive synchronization and control?????
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一个三元非线性二次项分数阶混沌系统的研究和控制
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