Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systems

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Stochastically forced discrete dynamical systems are considered. Using first approximation systems, we study dynamics of deviations of stochastic solutions from deterministic equilibria. Necessary and sufficient conditions of the existence of stable stationary solutions of equations for mean-square deviations are derived. Stationary values of these mean-square deviations are used for the estimations of the dispersion of random states nearby stable equilibria and analysis of noise-induced transitions. Constructive application of the suggested technique to the analysis of various stochastic regimes in Ricker population model with Allee effect is demonstrated.

Keywords: nonlinear discrete systems, random disturbances, noise-induced transitions, Ricker model
Citation in English: Bashkirtseva I.A. Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systems // Computer Research and Modeling, 2013, vol. 5, no. 4, pp. 559-571
Citation in English: Bashkirtseva I.A. Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systems // Computer Research and Modeling, 2013, vol. 5, no. 4, pp. 559-571
DOI: 10.20537/2076-7633-2013-5-4-559-571
According to Crossref, this article is cited by:
  • Ekaterina Dmitrievna Ekaterinchuk, Lev Borisovich Ryashko. Analysis of stochastic attractors for time-delayed quadratic discrete model of population dynamics. // Computer Research and Modeling. 2015. — V. 7, no. 1. — P. 145. DOI: 10.20537/2076-7633-2015-7-1-145-157
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