控制周期激励Van der Pol-Duffing振子的混沌

The control over the periodically excited Van der Pol-Duffing

对周期激励VanderPol-Duffing振子进行了研究:x··-μ(1-x2)x·-αx+βx3=fcosωt。首先运用相图分析、直接观察运动时间序列的方法发现,VanderPol-Duffing振子在一定条件下会出现混沌行为。在实际工程中,混沌行为往往会导致振荡或不规则运动,甚至主系统的彻底崩溃,因此有必要抑制系统的混沌行为。文中采用周期激振力法对系统中的混沌行为进行了控制,并结合lyapunov指数谱进行了分析,结果表明VanderPol-Duffing振子中的混沌运动得到了有效的控制。

The periodically excited Van der Pol-Duffing Oscillator is described as follows:\%x\{··\}-μ(1-x^2)x·-αx+βx^3=f\%cos\% ωt\%. The chaotic behaviours of the system are examined with phase portraits and time history observations. Periodical exciting force method is used to suppress the chaotic motions of the system and Lyapunov exponents are applied in the analysis. The calculator simulations show that the chaos of the above system can be controlled effectively by adjusting proper controlling signals.