Projective Synchronization for a Class of Fractional-Order Chaotic Systems with Fractional-Order in the (1, 2) Interval

Abstract

Abstract:In this paper, a projective synchronization approach for a class of fractional-order chaotic systems with fractional-order 1 < q < 2 is demonstrated. The projective synchronization approach is established through precise theorization. To illustrate the effectiveness of the proposed scheme, we discuss two examples: (1) the fractional-order Lorenz chaotic system with fractional-order q = 1.1; (2) the fractional-order modified Chua's chaotic system with fractional-order q = 1.02. The numerical simulations show the validity and feasibility of the proposed scheme.

Some Remarks on Estimate of Mittag-Leffler Function

“…Obviously, the correctness of the estimate of Mittag-Leffler function is crucial to the whole estimation process and plays an important role if the estimation based method is adopted. Recently, estimation based method has been widely applied to the study of finite-time stability and synchronization of fractionalorder memristor-based neural networks [1][2][3][4][5][6][7], stability and stabilization of nonlinear fractional-order systems [8][9][10][11][12][13], finite-time stability of fractional-order neural networks [14,15], synchronization of fractional-order chaotic systems [16], consensus analysis of fractional-order multiagent systems [17][18][19], etc. The estimate on Mittag-Leffler function was first proposed in [20].…”

A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos

“…Now, it is well-known that many real-world physical systems [1][2][3][4] can be more accurately described by fractional-order differential equations, for example, dielectric polarization, viscoelasticity, electrode-electrolyte polarization, electromagnetic waves, diffusion-wave, superdiffusion, heat conduction. Meanwhile, chaotic behavior has been found in many fractional-order systems like the fractional-order brushless DC motor chaotic system [5,6], the fractional-order gyroscopes chaotic system [7], the fractional-order microelectromechanical chaotic system [8], the fractional-order electronic circuits [9,10], and so forth [11][12][13][14][15][16].…”

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

“…The adopted synchronization schemes include adaptive control [30][31][32], backstepping control [33], fuzzy control [8], impulsive control [34,35], etc. The realized synchronization types include complete synchronization [36,37], anti-synchronization [32], projective synchronization [23,38], lag synchronization [24,39], combination synchronization [40,41], compound synchronization [10], etc. However, to our best knowledge, memristor-based complex systems are not involved in the existing literature, unfortunately.…”