Bashkirtseva Irina, Ryazanova Tatyana, Ryashko Lev
Department of Mathematics, Ural Federal University, Lenina 51, Ekaterinburg, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042908. doi: 10.1103/PhysRevE.92.042908. Epub 2015 Oct 5.
We study a stochastic dynamics of systems with hard excitement of auto-oscillations possessing a bistability mode with coexistence of the stable equilibrium and limit cycle. A principal difference in the results of the impact of additive and parametric random disturbances is shown. For the stochastic van der Pol oscillator with increasing parametric noise, qualitative transformations of the probability density function form "crater"-"peak+crater"-"peak" are demonstrated by numerical simulation. An analytical investigation of such P bifurcations is carried out for the stochastic Hopf-like model with hard excitement of self-oscillations. A detailed parametric description of the response of this model on the additive and multiplicative noise and corresponding stochastic bifurcations are presented and discussed.
我们研究了具有自激振荡硬激励的系统的随机动力学，该系统具有稳定平衡和极限环共存的双稳模式。展示了加性和参数随机扰动影响结果的主要差异。对于参数噪声增加的随机范德波尔振荡器，通过数值模拟证明了概率密度函数形式从“坑”到“峰 + 坑”再到“峰”的定性转变。对具有自激振荡硬激励的随机类霍普夫模型进行了此类P分岔的解析研究。给出并讨论了该模型对加性和乘性噪声响应的详细参数描述以及相应的随机分岔。
