Fractional-order Synchronization Research Articles

RBFNN-PSO Intelligent Synchronisation Method for Sprott B Chaotic Systems with External Noise and Its Application in an Image Encryption System.

In the past two decades, research in the field of chaotic synchronization has attracted extensive attention from scholars, and at the same time, more synchronization methods, such as chaotic master-slave synchronization, projection synchronization, sliding film synchronization, fractional-order synchronization and so on, have been proposed and applied to chaotic secure communication. In this paper, based on radial basis function neural network theory and the particle swarm optimisation algorithm, the RBFNN-PSO synchronisation method is proposed for the Sprott B chaotic system with external noise. The RBFNN controller is constructed, and its parameters are used as the particle swarm particle optimisation parameters, and the optimal values of the controller parameters are obtained by the PSO training method, which overcomes the influence of external noise and achieves the synchronisation of the master-slave system. Then, it is shown by numerical simulation and analysis that the scheme has a good performance against external noise. Because the Sprott B system has multiple chaotic attractors with richer dynamics, the synchronization system based on Sprott B chaos is applied to the image encryption system. In particular, the Zigzag disambiguation method for top corner rotation and RGB channel selection is proposed, and the master-slave chaotic system synchronisation sequences are diffused to the disambiguated data streams, respectively. Therefore, the encryption and decryption of image transmission are implemented and the numerical simulation results are given, the random distribution characteristics of encrypted images are analysed using histogram and Shannon entropy methods, and the final results achieve the expected results.

Synchronization of Incommensurate Fractional-Order Chaotic Systems Based on Linear Feedback Control

The dynamics and synchronization of fractional-order (FO) chaotic systems have received much attention in recent years. However, the research are focused mostly on FO commensurate systems. This paper addresses the synchronization of incommensurate FO (IFO) chaotic systems. By employing the comparison principle for FO systems with multi-order and the linear feedback control method, a sufficient condition for ensuring the synchronization of IFO chaotic systems is developed in terms of linear matrix inequalities (LMIs). Such synchronization condition relies just on the system parameters, and is easily verify and implemented. Two typical FO chaotic systems, named the IFO Genesio-Tesi system and Hopfied neural networks are selected to demonstrate the effectiveness and feasibility of the proposed method.

Robust non‐fragile Mittag‐Leffler synchronization of fractional order non‐linear complex dynamical networks with constant and infinite distributed delays

The present article is an attempt to investigate the robust non‐fragile Mittag‐Leffler synchronization of fractional order non‐linear complex dynamical networks with uncertain parameters and mixed delays. First, we develop a generalized fractional order complex dynamical network (GFOCDN) and then derive its synchronization criteria by using certain Lemmas based on the theory of Lyapunov stability and, second, by adding parameters of uncertainty to the GFOCDN and derive the synchronization analysis by including the appropriate non‐fragile controller into the system model to achieve a non‐fragile Mittag‐Leffler synchronization. Third, we incorporate the parameter uncertainty into the inner couplings and derive as a special case to achieve its synchronization. Finally, we present two numerical simulations to show the reliability of our proposed work.

Chaos control and synchronization of fractional order delay‐varying computer virus propagation model

In the present article, the authors have studied the dynamical behavior of delay‐varying computer virus propagation (CVP) model with fractional order derivative, and it is found that the chaotic attractor exists in the considered fractional order system. In order to eliminate the chaotic behavior of fractional order delay‐varying CVP model, feedback controlmethod is used. This article also dealswith the synchronization between controlled and chaotic delay‐varying CVPmodel via active controlmethod. The fractional derivative is described in the Caputo sense. Numerical simulation results are carried out by means of Adams‐Boshforth‐Moultonmethod with the help ofMATLAB, and the results are successfully depicted through graphs .Copyright © 2015 John Wiley & Sons, Ltd.

Hybrid Projective Synchronization of Different Fractional Order Hyperchaotic Systems

This paper investigated hybrid projective synchronization of fractional order hyperchaotic systems with different orders. Based on the idea of active control and the stability theory of linear fractional-order system, we design the effective controller to realize the hybrid projective synchronization. Numerical simulation results which are carried show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order hyperchaotic systems while it also allows both the systems to remain in hyperchaotic states.