Hopf bifurcation control for delayed complex networks

In this paper, we consider the problem of Hopf bifurcation control for a complex network model with time delays. We know that for the system without control, as the positive gain parameter of the system passes a critical point, Hopf bifurcation occurs. To control the Hopf bifurcation, a time-delayed feedback controller is proposed to delay the onset of an inherent bifurcation when such bifurcation is undesired. Furthermore, we can also change the stability and direction of bifurcating periodic solutions by choosing appropriate control parameters. Numerical simulation results confirm that the new feedback controller using time delay is efficient in controlling Hopf bifurcation.     

Dynamical behavior in a harvested differential-algebraic prey-predator model with discrete time delay and stage structure

A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, the dynamic behaviors of the proposed model system with and without discrete time delay are investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; on the other hand, the local stability of the model system with discrete time delay is also studied. The theoretical analysis shows that the discrete time delay has a destabilizing effect in the model of population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Numerical simulations are carried out to show the consistency with theoretical analysis.     

一类三维动力系统的分岔及混沌分析

对一类三维非线性混沌金融系统进行了动力学特征分析,得到了模型方程的三个平衡点,并对其稳定性进行了讨论.通过数值仿真得到了系统的分岔图及Lyapunov 指数图,进而分析了参数变化对系统稳定性及分岔的影响.该研究对理解各种金融政策的杠杆原理有参考意义.     

一个混沌纠缠系统的动力学分析

通过一系列动力学分析,验证了一个纠缠系统是混沌的.当混沌纠缠实现时,所有的平衡点是不稳定的鞍结点.数值计算显示这个系统有一个正的Lyapunov指数,这表明该系统是混沌的.通过局部放大的分岔图验证了系统由倍周期分岔通向混沌的过程,并分析了该混沌系统的Hopf分岔现象.