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Bifurcations in stochastic dynamical systems with simple singularities

  • Janeczko, Stanisaw
  • Wajnryb, Eligiusz
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    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.

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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 31 (1989)
    Issue (Month): 1 (March)
    Pages: 71-88

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    Handle: RePEc:eee:spapps:v:31:y:1989:i:1:p:71-88
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