On chaos control and synchronization of the commensurate fractional order Liu system

2013 ◽  
Vol 18 (5) ◽  
pp. 1193-1202 ◽  
Author(s):  
A.S. Hegazi ◽  
E. Ahmed ◽  
A.E. Matouk
Keyword(s):  
Fractional Order ◽  
Chaos Control ◽  
Control And Synchronization ◽  
Liu System

scholarly journals The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Runzi Luo ◽  
Haipeng Su
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
External Disturbances ◽  
Numerical Examples ◽  
Single Output ◽  
Lorenz Chaotic System ◽  
Control And Synchronization

This paper investigates the stabilization and synchronization of a class of fractional-order chaotic systems which are affected by external disturbances. The chaotic systems are assumed that only a single output can be used to design the controller. In order to design the proper controller, some observer systems are proposed. By using the observer systems some sufficient conditions for achieving chaos control and synchronization of fractional-order chaotic systems are derived. Numerical examples are presented by taking the fractional-order generalized Lorenz chaotic system as an example to show the feasibility and validity of the proposed method.

scholarly journals Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2)

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
A. Al-khedhairi ◽  
S. S. Askar ◽  
A. E. Matouk ◽  
A. Elsadany ◽  
M. Ghazel
Keyword(s):  
Fractional Order ◽  
Chaos Control ◽  
Control Method ◽  
Control Technique ◽  
Linear Feedback ◽  
Nonlinear Feedback ◽  
Population System ◽  
Wide Range ◽  
Control And Synchronization ◽  
Fractional Parameter

This paper demonstrates dynamics, chaos control, and synchronization in Samardzija-Greller population model with fractional order between zero and two. The fractional-order case is shown to exhibit rich variety of nonlinear dynamics. Lyapunov exponents are calculated to confirm the existence of wide range of chaotic dynamics in this system. Chaos control in this model is achieved via a novel linear control technique with the fractional order lying in (1, 2). Moreover, a linear feedback control method is used to control the fractional-order model to its steady states when 0<α<2. In addition, the obtained results illustrate the role of fractional parameter on controlling chaos in this model. Furthermore, nonlinear feedback synchronization scheme is also employed to illustrate that the fractional parameter has a stabilizing role on the synchronization process in this system. The analytical results are confirmed by numerical simulations.

scholarly journals Chaos Control and Synchronization in Fractional-Order Lorenz-Like System

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Sachin Bhalekar
Keyword(s):  
Dynamical System ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Stable Region ◽  
Linear Feedback ◽  
Effective Dimension ◽  
Nonlinear Feedback ◽  
Linear Feedback Controller ◽  
Control And Synchronization

The present paper deals with fractional-order version of a dynamical system introduced by Chongxin et al. (2006). The chaotic behavior of the system is studied using analytic and numerical methods. The minimum effective dimension is identified for chaos to exist. The chaos in the proposed system is controlled using simple linear feedback controller. We design a controller to place the eigenvalues of the system Jacobian in a stable region. The effectiveness of the controller in eliminating the chaotic behavior from the state trajectories is also demonstrated using numerical simulations. Furthermore, we synchronize the system using nonlinear feedback.

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