非自治范德波振子的随机振动

Stochastic Vibration of Non-Autonomous Van Der Pol Oscillator

利用数值模拟方法对非自治范德波振子 (NAVDPO)进行模拟 ,获得了NAVDPO的概率密度流及其位移 -速度联合概率密度流 ,发现NAVDPO存在复杂的时间分岔 ,也存在复杂的结构分岔 .它的演变可以是单峰状态 ,也可以是多峰状态 .NAVDPO的联合概率密度存在孤立的四峰 ,对应复杂的跳跃运动 .文中分析了这些特征的性质和意义 .

In this paper, the numerical simulation technique is applied to analyze the pro_perty of the non_autonomous Van Der Pol oscillator (NAVDPO) which is subjected to both period and noise forcing. The period non_stationary probability density flow and the sta te joint probability density flow are acquired for the first time. It shows that the probability density flow is constructed by both the “time bifurcation” and the “structure bifurcation” which have complicate structure. The evolution of NAVDPO may follow either a sing le _peak pattern or a multi_peak pattern. It also shows that there are four solitary peaks of state_joint probability density on a rhombus limit cycle on the state space at every time, thus bringing about complicated jump motion in NAVDPO. The properties and meaning of these phenomena are also discussed