Projective synchronization between different fractional-order hyperchaotic systems with uncertain parameters using proposed modified adaptive projective synchronization technique

Abstract

In the present article, the authors have proposed a modified projective adaptive synchronization technique for fractional‐order chaotic systems. The adaptive projective synchronization controller and identification parameters law are developed on the basis of Lyapunov direct stability theory. The proposed method is successfully applied for the projective synchronization between fractional‐order hyperchaotic Lü system as drive system and fractional‐order hyperchaotic Lorenz chaotic system as response system. A comparison between the effects on synchronization time due to the presence of fractional‐order time derivatives for modified projective synchronization method and proposed modified adaptive projective synchronization technique is the key feature of the present article. Numerical simulation results, which are carried out using Adams–Boshforth–Moulton method show that the proposed technique is effective, convenient and also faster for projective synchronization of fractional‐order nonlinear dynamical systems. Copyright © 2013 John Wiley & Sons, Ltd.

Fractional matrix and inverse matrix projective synchronization methods for synchronizing the disturbed fractional‐order hyperchaotic system

“…Since the introduction of the synchronization for two chaotic signals starting at different initial conditions, more and more attention has been devoted to the control and synchronization for the chaotic and fractional‐order chaotic systems. Moreover, the types of synchronization are extended to complete synchronization, antisynchronization, phase synchronization, generalized synchronization, projective synchronization, and so on. In order to achieve these synchronizations, various synchronization methods such as linear and nonlinear feedback control, active control, adaptive control, sliding‐mode control, and backstepping design technique have been successfully used for the chaotic and fractional‐order chaotic systems.…”

“…Among all types of chaotic synchronizations, projective synchronization, which is characterized by the fact that the drive and response systems could be synchronized up to a scaling factor, has been widely applied in many fields. However, to our best knowledge, most of the literary works have study the projective synchronization whose scaling factor is a fixed constant or a diagonal matrix, which is lack of generality; additionally, because of the complexity and uncertainty of the fractional and nonlinear problem, the fractional nonlinear dynamical model also has uncertainty, but many previous studies do not take into account the influence of the model parameter's uncertainty and external disturbance, which cannot be avoided in real applications; thus, in this paper, we will focus on presenting the general method for synchronizing the actual fractional‐order hyperchaotic systems disturbed by model uncertainties and external disturbances, ie, the fractional matrix and inverse matrix projective synchronization methods. The remaining of this paper is organized as follows.…”

Dynamic Analysis of Complex Synchronization Schemes between Integer Order and Fractional Order Chaotic Systems with Different Dimensions

“…Complete synchronization (CS), projective synchronization (PS), full state hybrid function projective synchronization (FSHFPS), and generalized synchronization (GS) are effective approaches to achieve synchronization and have been used widely in integer order chaotic systems [32][33][34][35] and fractional order chaotic systems [36][37][38][39]. Studying inverse problems of synchronization is an attractive and important idea.…”

A robust method for new fractional hybrid chaos synchronization

“…So far, a wide variety of approaches and techniques have been proposed for the synchronization of the fractionalorder chaotic such as sliding mode controller [11][12][13], active and adaptive controllers [14][15][16], feedback control [17,18], linear and nonlinear methods [19,20], scalar signal technique [21,22]. Also, many types of synchronization for the fractional-order chaotic systems have been presented, such as complete synchronization [23], anti-synchronization [24], projective synchronization [25], full state hybrid projective synchronization [26], phase synchronization [27,28] , finite-time synchronization [29]. Amongst all kinds of chaos synchronization, generalized synchronization (GS) is one of the most noticeable one.…”