Abstract
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” are demonstrated by numerical simulation. An analytical investigation of such 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.
5 More- Received 16 June 2015
DOI:https://doi.org/10.1103/PhysRevE.92.042908
©2015 American Physical Society