Bifurcations in stochastic dynamical systems with simple singularities
type: Item
instance of: scholarly article
title: Bifurcations in stochastic dynamical systems with simple singularities
zbMATH Open document ID: 0714.60068
DOI: 10.1016/0304-4149(89)90103-8
author: Stanisław Janeczko
author: Eligiusz Wajnryb
published in: Stochastic Processes and their Applications
publication date: 1989-01-01T00:00:00Z
review text: The paper deals only with 1-dimensional stochastic dynamical system. In Section 2, some necessary preliminaries concerning stochastic dynamical systems driven by the dichotomous Markov noise are given and a geometric method to investigate their probability densities is proposed. Section 3 is devoted to a presentation of various physical systems with stochastic noise, for example, the generalized Langevin system, the dye laser system with pre-Gaussian pump fluctuations. Equations for the stationary probability are shown. In Section 4, the theory for stable dynamical systems with a stochastic control space is developed and some properties are proved. The equations for stationary probability densities are reduced to equations with so-called singular points. In Section 5, the analysis of bifurcation diagrams for stable dynamical systems is provided. The fold model and the cusp model with dichotomous noise are investigated and the corresponding bifurcation diagrams are obtained.
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 93E03
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 4176159
zbMATH Keywords: physical systems with stochastic noise
zbMATH Keywords: generalized Langevin system
zbMATH Keywords: stationary probability
zbMATH Keywords: stochastic control
zbMATH Keywords: bifurcation diagrams
reviewed by: T. Sasagawa
MaRDI profile type: Publication
full work available at URL: 0304-4149(89)90103-8
OpenAlex ID: W2140086882
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description: scientific article; zbMATH DE number 4176159