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Bifurcations in stochastic dynamical systems with simple singularities

Author

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  • Janeczko, Stanisaw
  • Wajnryb, Eligiusz

Abstract

The generalized Langevin stochastic dynamical system is introduced and the stationary probability density for its solution is investigated. The stochastic field is assumed to be singular with a simple singularity, and noise in the control parameters is modelled as dychotomous Markov noises. A classification of bifurcation diagrams for the stationary density probability is obtained. Two examples encountered from physics, the dye laser model and the Verhulst model, are investigated.

Suggested Citation

  • Janeczko, Stanisaw & Wajnryb, Eligiusz, 1989. "Bifurcations in stochastic dynamical systems with simple singularities," Stochastic Processes and their Applications, Elsevier, vol. 31(1), pages 71-88, March.
    • Handle: RePEc:eee:spapps:v:31:y:1989:i:1:p:71-88
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