Shihua Chen

Synchronizing strict-feedback and general strict-feedback chaotic systems via a single controller

Abstract We present a systematic design procedure to synchronize a class of chaotic systems in a so-called strict-feedback form based on back-stepping procedure. This approach needs only a single controller to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, we point out that the method does not work for general strict-feedback chaotic systems, for instance, Lorenz system. Therefore, we propose three kinds of synchronization schemes for Lorenz system using the Lyapunov function method. All the three schemes avoid including divergence factor as in Ref. [Chaos, Solitons & Fractals 16 (2003) 37]. Especially in the last two schemes, we need only one state variable in controller, which has important significance in chaos synchronization used for communication purposes. Finally numerical simulations are provided to show the effectiveness and feasibility of the developed methods.

Upper and lower solution method for fourth-order four-point boundary value problems

This paper is concerned with the fourth-order ordinary differential equation u(4)(t) = f(t, u(t), u(t)), 0 0. Some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique.

Synchronizing strict-feedback chaotic system via a scalar driving signal

We propose a systematic design procedure to synchronize a class of chaotic system in a so-called strict-feedback form based on back-stepping procedure. This approach needs only a scalar driving signal to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, the numerical simulation with Chuas chaotic circuit verifies the effectiveness of the method.

Synchronization of impulsively coupled complex systems with delay

This paper investigates the synchronization of complex systems with delay that are impulsively coupled at discrete instants only. Based on the comparison theorem of impulsive differential system, a distributed impulsive control scheme is proposed to achieve the synchronization for systems with delay. In the control strategy, the influence of all nodes to network synchronization relies on its weight. The proposed control scheme is applied to the chaotic delayed Hopfield neural networks and numerical simulations are presented to demonstrate the effectiveness of the proposed scheme.

Outer Synchronization of Complex Networks by Impulse

This paper investigates outer synchronization of complex networks, especially, outer complete synchronization and outer anti-synchronization between the driving network and the response network. Employing the impulsive control method which is uncontinuous, simple, efficient, low-cost and easy to implement in practical applications, we obtain some sufficient conditions of outer complete synchronization and outer anti-synchronization between two complex networks. Numerical simulations demonstrate the effectiveness of the proposed impulsive control scheme.

Cooperative spreading processes in multiplex networks

This study is concerned with the dynamic behaviors of epidemic spreading in multiplex networks. A model composed of two interacting complex networks is proposed to describe cooperative spreading processes, wherein the virus spreading in one layer can penetrate into the other to promote the spreading process. The global epidemic threshold of the model is smaller than the epidemic thresholds of the corresponding isolated networks. Thus, global epidemic onset arises in the interacting networks even though an epidemic onset does not arise in each isolated network. Simulations verify the analysis results and indicate that cooperative spreading processes in multiplex networks enhance the final infection fraction.

A remark on stationary distribution of a stochastic SIR epidemic model with double saturated rates

Abstract In this paper, we propose and discuss a stochastic SIR epidemic model with saturated treatment and incidence rates. The existence and uniqueness of the global positive solution are achieved. By constructing suitable Lyapunov functions and using Khasminskii’s theory, we establish appropriate conditions to prove that the stochastic model has a unique stationary distribution and the ergodicity holds. Moreover, sufficient conditions that guarantee the epidemic disease’s extinction are given.

A unified framework of interplay between two spreading processes in multiplex networks

Different spreading processes may interplay and display rich intertwined effects in multiplex networks. In this study, a model is proposed that consists of a two-layer network and two spreading processes respectively spread by each layer. The proposed framework can unify three scenarios for various mutual influences between the two spreading processes. The epidemic thresholds of interacting networks are contrasted and proven using the corresponding isolated networks for three scenarios: competing spreading processes, cooperative spreading processes and the combination of the two. The following conclusions resulted from this work with these three scenarios. First, the epidemic threshold of the interacting two-layer networks can be increased for two competing spreading processes; second, the epidemic threshold of the interacting two-layer networks can be decreased for two cooperative spreading processes; third, when the spreading process in one layer restrains the spreading process in the other layer, and the spreading process in the latter reinforces that in the former, the epidemic threshold of the former layer can be increased and that of the latter layer can be decreased for the interacting networks in comparison to the corresponding isolated networks. Simulations accurately verified the stated results.

A novel hybrid synchronization of two coupled complex networks

This paper deals with the hybrid synchronization problem of two coupled complex networks. By using the linear feedback controller, several useful hybrid synchronization criteria of two coupled networks are obtained based on the Lyapunov stability theory and Lasalles invariant principle. Analytical results also show that two coupled complex networks can realize hybrid synchronization under suitable conditions. Numerical simulations are then given to verify the effectiveness of the proposed hybrid synchronization scheme.

A new non-autonomous model for migratory birds with LeslieGower Holling-type II schemes and saturation recovery rate

Migratory birds are essential factors in the epidemiology of infectious diseases. This article discusses a new predatorprey model for susceptible migratory birds, infected migratory birds and predator species. Time-dependent coefficients are considered with the LeslieGower Holling-type II schemes and the saturated recovery rate in this new model. Some sufficient conditions for the extinction and permanence of diseases are established on the basis of relatively weak assumptions. The global attractiveness of the model is also given through spectral analysis and Liapunov function. Our results reveal that the infective species is extinct if the upper threshold value R1, whereas the model is permanent if the lower threshold value R>1. Numerical simulations are conducted to confirm the obtained results.