非自治范德波振子的随机振动

利用数值模拟方法对非自治范波振子（ＮＡＶＤＰＯ）进行模拟,获得了ＮＡＶＤＰＯ的概率密度流及其位移－速度联合速率密度流,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,文中分析了这些行征的性质和意义。

Stochastic Vibration of Non-Autonomous Van Der Pol Oscillator

Inthis paper, the numerical simulation technique is applied to analyze the pro_perty of thenon_autonomous Van Der Pol oscillator (NAVDPO) which is subjected to both period and noiseforcing. The period non_stationary probability density flow and the sta-te-jointprobability density flow are acquired for the first time. It shows that the probabilitydensity flow is constructed by both the “time bifurcation” and the “structure bifurcation” which have complicate structure. The evolution of NAVDPOmay follow either a sing-le_peak pattern or a multi_peak pattern. It also shows that thereare four solitary peaks of state_joint probability density on a rhombus limit cycle on thestate space at every time, thus bringing about complicated jump motion in NAVDPO. Theproperties and meaning of these phenomena are also discussed