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Stochastic bifurcations caused by multiplicative noise in systems with hard excitement of auto-oscillations
Irina Bashkirtseva1, Tatyana Ryazanova1, Lev Ryashko1
1Department of Mathematics, Ural Federal University, Lenina 51, Ekaterinburg, Russia.
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+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.
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