Vijay K. Yadav

Comparative study of synchronization methods of fractional order chaotic systems

Abstract In this article, the active control method and the backstepping method are used during the synchronization of fractional order chaotic systems. The salient feature of the article is the analysis of time of synchronization between fractional order Chen and Qi systems using both the methods. Numerical simulation and graphical results clearly exhibit that backstepping approach is better than active control method for synchronization of the considered pair of systems, as it takes less time to synchronize while using the first one compare to second one.

Backstepping Control for Combined Function Projective Synchronization Among Fractional Order Chaotic Systems with Uncertainties and External Disturbances

In the present chapter the combined function projective synchronization among fractional order chaotic systems in the presence of uncertain parameters and external disturbances using backstepping control method is investigated. The chaotic attractors of the systems are found for fractional-order time derivative, which is described in Caputo sense. A new lemma of Caputo derivatives is used to design the controller based on Lyapunov stability theory. During the combined function projective synchronization among the non-identical fractional order systems, the Lorenz, Rossler and Chen systems are taken to illustrate the effectiveness of the considered method. Numerical simulation and graphical results for different particular cases clearly exhibit that the method with this new procedure is easy to implement and reliable for synchronization of non-identical fractional order chaotic systems.

Dual Combination Synchronization Scheme for Nonidentical Different Dimensional Fractional Order Systems Using Scaling Matrices

Abstract In this chapter the dual combination synchronization has been studied among different dimensional fractional order systems by using scaling matrices. The dual combination synchronization scheme for different dimensional fractional order systems is also developed. The fractional order time derivative is described in Caputo sense. During synchronization the control functions are designed based on fractional order Lyapunov stability theory and using a new lemma which is given for fractional order Lyapunov function. Numerical simulation and graphical results clearly exhibit that the proposed procedure is easy to implement and reliable for dual combination synchronization for nonidentical and different dimensional fractional order chaotic systems.