Jianwen Feng

Synchronization between two Different Fractional-order Chaotic Systems

This paper studies chaos synchronization between two different fractional-order chaotic systems using an active control method. In particular, the technique is applied to achieve chaos synchronization for each pair of the Lorenz, Lü, and Chen fractional-order differential systems. Some theoretical results on synchronization are derived using Laplace transformation theory. Finally, numerical simulations are used to demonstrate the effectiveness of this technique.

Cluster Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control

We consider a method for driving general complex networks into prescribed cluster synchronization patterns by using pinning control. The coupling between the vertices of the network is nonlinear, and sufficient conditions are derived analytically for the attainment of cluster synchronization. We also propose an effective way of adapting the coupling strengths of complex networks. In addition, the critical combination of the control strength, the number of pinned nodes and coupling strength in each cluster are given by detailed analysis cluster synchronization of a special topological structure complex network. Our theoretical results are illustrated by numerical simulations.

Designing lag synchronization schemes for unified chaotic systems

Abstract Lag synchronization of chaotic unified systems is investigated theoretically and numerically. Three kinds of single-controller schemes are designed to achieve lag synchronization of the so-called chaotic unified systems and some results are proved theoretically using Lyapunov’s stability theory. Computer simulations are then provided to show the effectiveness and feasibility of the proposed methods.

Generalized Projective Synchronization between Two Different Neural Networks with Mixed Time Delays

The generalized projective synchronization (GPS) between two different neural networks with nonlinear coupling and mixed time delays is considered. Several kinds of nonlinear feedback controllers are designed to achieve GPS between two different such neural networks. Some results for GPS of these neural networks are proved theoretically by using the Lyapunov stability theory and the LaSalle invariance principle. Moreover, by comparison, we determine an optimal nonlinear controller from several ones and provide an adaptive update law for it. Computer simulations are provided to show the effectiveness and feasibility of the proposed methods.

Adaptive Synchronization of Uncertain Genesio Chaotic Systems Based on Parameter Identification

In this paper, the problem of chaos synchronization of Genesio systems with uncertain parameters is considered. A novel adaptive control scheme is proposed based on parameter identification. The novelty of our design is that we regard the unknown system parameters of the slave system as functions varying with time and we design the synchronization controller to make these functions converge to the exact parameters values of the master system in the synchronization process. Thus, we can achieve Genesio chaotic system synchronization and identify all unknown parameters simultaneously by this method. Finally, numerical simulation results are presented to show the effectiveness of the techniques.

Finite-time synchronization for nonlinearly coupled networks with time-varying delay

In this paper, nonlinearly coupled network with time-varying delay is considered. By using a class of simple discontinuous state feedback controllers, criteria for guaranteeing the finite-time synchronization of the complex dynamical network are derived based on the new analysis techniques. Its worth pointing out that the setting time to achieve synchronization is estimated, which depends on not only the initial value but the time-varying delay. Finally, several examples are presented to show the effectiveness and correction of the theoretical results we obtained in this paper.

Pinning Two Nonlinearly Coupled Complex Networks with an Asymmetrical Coupling Matrix

This paper addresses the hybrid synchronization problem in two nonlinearly coupled complex networks with asymmetrical coupling matrices under pinning control schemes. The hybrid synchronization of two complex networks is the outer antisynchronization between the driving network and the response network while the inner complete synchronization in the driving network and the response network. We will show that only a small number of pinning feedback controllers acting on some nodes are effective for synchronization control nof the mentioned dynamical networks. Based on Lyapunov Stability Theory, some simple criteria for hybrid nsynchronization are derived for such dynamical networks by pinning control strategy. Numerical examples nare provided to illustrate the effectiveness of our theoretical results.

Single Impulsive Controller for Exponential Synchronization of Stochastic Lur'e Networks with Impulsive Disturbance

The investigations are made on the exponential synchronization of the stochastic Lure system with nonlinear coupling and impulsive disturbance. The impulsive effects in complex networks could play a positive or a negative role for synchronization. For the sake of simplification and efficiency, a single impulsive controller is designed to realize the synchronization of the impulsive dynamical network with nrespect to stabilizing and destabilizing impulsive effects. Sufficient conditions are derived to guarantee the realization of the exponential synchronization for all initial values by means of the Lyapunov stability ntheorem, the comparison principle, and the linear matrix inequalities (LMIs). Numerical simulations are given to support the validity of the analytical results.

On Synchronizability of Kleinberg Small World Networks

In this paper, the impact of edge-adding probability on both synchronizability and average path length of Klein berg small world networks is investigated. It could be seen from the analysis that two dimensional Klein berg small world networks have similar properties as NW small world networks but Klein berg small world network is more general, that is, the synchronizability becomes stronger as the edge-adding probability increases. Moreover, the average path length of Klein berg small world network decreases with the increasing edge-adding probability. And this phenomenon is verified by numerical simulations on a network of Lorenz oscillators. Then, it could be deduced from the phenomenon observed that compared with the small probabilities of longer distance of the edge-adding, the large probabilities of shorter distance of the edge-adding could achieve better synchronizability. This means the probabilities of the edge-adding play more important than the length of edge-adding to enhance the synchronizability of the small world network.

Synchronizing the Noise-Perturbed Rössler Hyperchaotic System via Sliding Mode Control

This paper investigates the synchronization problem between two unidirectionally-coupled Rössler hyperchaotic systems in the presence of noise perturbations. Sufficient conditions are obtained for synchronization by using a particularly simple linear sliding mode surface that is based on the sliding mode control concept. Only one controller function is needed to achieve synchronization in our present approach which makes it much easier to implement in contrast to many other synchronization schemes that require two or more controllers. Numerical simulation results are also included to illustrate the superior features of this new scheme.