Mackey-Glass时滞系统的稳定性与混沌控制

Stability and chaotic control of Mackey-Glass time-delayed system

研究了时滞对Mackey-Glass系统动力学的行为影响和混沌控制.首先,时滞反馈控制不能使系统的零平衡点控制为稳定的.对于非零平衡点,从系统线性化方程的特征方程根的分布入手,分别研究了具有单时滞和双时滞系统的线性稳定性.发现当系统中的时滞经过一系列临界值时,系统经历了Hopf分支.其次,应用时滞反馈控制方法,选择合适的反馈增益和时滞使系统在不稳定非零平衡点附近出现周期轨.最后,通过数值模拟检验了理论结果.

It is investigated that the effect of delay on dynamic behavior and chaotic control of MackeyGlass system.Firstly,we show that delayed feedback control cannot stabilize the origin.For non-zero equilibrium,the linear stabilities with one delay and two delays are respectively investigated by analyzing the distribution of the roots of associated characteristic equation.It is found that Hopf bifurcations exist when the delays pass through a sequence of critical values.Secondly,applying of delayed feedback control method,by designing appropriate feedback strength and delay,we show that the unstable equilibrium can be controlled to be stable bifurcating periodic solutions at the neighborhood of the equilibrium.Finally,some numerical simulations are carried out for supporting the analytic results.