Stochastic bifurcations caused by multiplicative noise in systems with hard excitement of auto-oscillations

Irina Bashkirtseva, Tatyana Ryazanova, and Lev Ryashko
Phys. Rev. E 92, 042908 – Published 5 October 2015

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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  • Received 16 June 2015

DOI:https://doi.org/10.1103/PhysRevE.92.042908

©2015 American Physical Society

Authors & Affiliations

Irina Bashkirtseva*, Tatyana Ryazanova, and Lev Ryashko

  • Department of Mathematics, Ural Federal University, Lenina 51, Ekaterinburg, Russia

  • *irina.bashkirtseva@urfu.ru
  • tatyana.ryazanova@urfu.ru
  • Corresponding author: lev.ryashko@urfu.ru

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Issue

Vol. 92, Iss. 4 — October 2015

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