Dawei Ding

Bifurcation control of complex networks model via PD controller

In this paper, we investigate the problem of bifurcation control for a complex networks in a small-world networks model with time delay. By choosing the nonlinear interactive parameter as the bifurcation parameter, we present a Proportional-Derivative (PD) feedback controller to control Hopf bifurcation which inherently happens due to the networks topology. Stability analysis shows that the onset of Hopf bifurcation can be delayed or advanced via a PD controller by setting proper control parameters. Therefore the Hopf bifurcation of the model became controllable to achieve desirable behaviors which is applicable in certain circumstances. Meanwhile, the direction and stability of bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Finally, numerical simulations confirm the effectiveness of the control strategy in controlling the Hopf bifurcation for the complex network model.

Hopf bifurcation control of congestion control model in a wireless access network

The main purpose of this paper is to analyze the problem of Hopf bifurcation control for a congestion control model in a wireless access network with time delay. By choosing communication delay as a bifurcation parameter, it is shown that when delay passes through a critical value, the Hopf bifurcation occurs. The bifurcation behavior may cause heavy oscillation and induce network instability. In order to control the undesirable Hopf bifurcation, a hybrid control strategy is proposed. By using a linear stability analysis, we show that adjusting the control parameters of the hybrid control strategy properly, the Hopf bifurcation can be delayed or even eliminated completely without changing the equilibrium point of the system. Therefore, this method can effectively control the Hopf bifurcation for the TCP/AQM wireless network model. Theoretical analysis and numerical simulation results show that this method is effective in controlling Hopf bifurcation of congestion control model in wireless network.

Bifurcation analysis in a delayed fractional neural network involving self-connection

Abstract The aim of this paper is to analyze the bifurcation for a fractional neural network with self-connection delay involving three neurons. First, by employing the characteristic equation, the bifurcation points of the proposed network are exactly calculated using time delay or the system parameter as a bifurcation parameter, respectively. Second, it is detected that fractional order is conducive to the bifurcation point for such network, and the onset of bifurcation can be markedly deferred or advanced. Third, the bifurcation diagrams are leerily plotted. Finally, to confirm the efficacy of the analytical results, some numerical simulations are rendered.

Hybrid control of delay induced hopf bifurcation of dynamical small-world network

In this paper, we focus on the Hopf bifurcation control of a small-world network model with time-delay. With emphasis on the relationship between the Hopf bifurcation and the time-delay, we investigate the effect of time-delay by choosing it as the bifurcation parameter. By using tools from control and bifurcation theory, it is proved that there exists a critical value of time-delay for the stability of the model. When the time-delay passes through the critical value, the model loses its stability and a Hopf bifurcation occurs. To enhance the stability of the model, we propose an improved hybrid control strategy in which state feedback and parameter perturbation are used. Through linear stability analysis, we show that by adjusting the control parameter properly, the onset of Hopf bifurcation of the controlled model can be delayed or eliminated without changing the equilibrium point of the model. Finally, numerical simulations are given to verify the theoretical analysis.

Adaptive Synchronization of Fractional Order Complex-Variable Dynamical Networks via Pinning Control*

In this paper, the synchronization of fractional order complex-variable dynamical networks is studied using an adaptive pinning control strategy based on close center degree. Some effective criteria for global synchronization of fractional order complex-variable dynamical networks are derived based on the Lyapunov stability theory. From the theoretical analysis, one concludes that under appropriate conditions, the complex-variable dynamical networks can realize the global synchronization by using the proper adaptive pinning control method. Meanwhile, we succeed in solving the problem about how much coupling strength should be applied to ensure the synchronization of the fractional order complex networks. Therefore, compared with the existing results, the synchronization method in this paper is more general and convenient. This result extends the synchronization condition of the real-variable dynamical networks to the complex-valued field, which makes our research more practical. Finally, two simulation examples show that the derived theoretical results are valid and the proposed adaptive pinning method is effective.

Hybrid Control of Bifurcation in XCP

In this paper, the nonlinear dynamical of explicit Control Protocol (XCP) for Internet congestion control system is investigated, a new hybrid control strategy is proposed, in which state feedback and parameter perturbation are used to control the bifurcations of XCP systems. Theoretical analysis and numerical simulations confirm that our method is efficient in controlling Hopf bifurcation of the XCP system.