Mayank Srivastava

Reduced-order anti-synchronization of the projections of the fractional order hyperchaotic and chaotic systems

The article aims to study the reduced-order anti-synchronization between projections of fractional order hyperchaotic and chaotic systems using active control method. The technique is successfully applied for the pair of systems viz., fractional order hyperchaotic Lorenz system and fractional order chaotic Genesio-Tesi system. The sufficient conditions for achieving anti-synchronization between these two systems are derived via the Laplace transformation theory. The fractional derivative is described in Caputo sense. Applying the fractional calculus theory and computer simulation technique, it is found that hyperchaos and chaos exists in the fractional order Lorenz system and fractional order Genesio-Tesi system with order less than 4 and 3 respectively. The lowest fractional orders of hyperchaotic Lorenz system and chaotic Genesio-Tesi system are 3.92 and 2.79 respectively. Numerical simulation results which are carried out using Adams-Bashforth-Moulton method, shows that the method is reliable and effective for reduced order anti-synchronization.

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.