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Stability Analysis, Chaos control of Fractional Order Vallis and El-Nino Systems and Their Synchronization

IEEE/CAA Journal of Automatica Sinica 2017年第1期4卷 114-124页

作者： Subir Das Vijay K Yadav Department of Mathematical Sciences Indian Institute of Technology Banaras Hindu University

In this article the authors have studied the stability analysis and chaos control of the fractional order Vallis and El-Nino systems. The chaos control of these systems is studied using nonlinear control method with the help of a new lemma for Caputo derivative and Lyapunov stability *** synchronization between the systems for different fractional order cases and numerical simulation through graphical plots for different particular cases clearly exhibit that the method is easy to implement and reliable for synchronization of fractional order chaotic systems. The comparison of time of synchronization when the systems pair approaches from standard order to fractional order is the key feature of the article.

关键词： El-Nino system fractional derivative nonlinear control method stability analysis synchronization Vallis systems

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Modified Projective Synchronization of a New Hyperchaotic System via nonlinear control

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Communications in Theoretical Physics 2009年第8期52卷 274-278页

作者： LI Xin Department of Mathematics Changshu Institute .of Technology Changshu 215500 China

In this paper, a nonlinear control scheme of two identical hyperchaotic Chert systems is developed to realize their modified projective synchronization. We achieve modified projective synchronization between the two identical hyperchaotic systems by directing the scaling factor onto the desired value. With symbolic computation system Maple and Lyapunov stability theory, numerical simulations are given to perform the process of the synchronization.

关键词： modified projective synchronization nonlinear control method hyperchaotic Chen system

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control and Synchronization with Known and Unknown Parameters

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Applied Mathematics 2016年第3期7卷 292-303页

作者： Maysoon M. Aziz Saad Fawzi Al-Azzawi Department of Mathematics College of Computer Sciences and Mathematics University of Mosul Mosul Iraq

In this paper, we consider the chaos control for 4D hyperchaotic system by two cases, known & unknown parameters based on Lyapunov stability theory via nonlinear control. We find that there are two cofactors that have an effect on determining any case to achieve the control, the two cofactors are proposed in the control and the matrix that produce from the time derivative of Lyapunov function. In adding, we find some weakness cases in Lyapunov stability theory. For this reason, we design with only one controller and perform a simple change in this control in order to recognize the difference between these cases although all of the controllers are almost similar.

关键词： 4D Hyperchaotic System control Synchronization Lyapunov Stability Theory nonlinear control method

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