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Stochastic sensitivity of cycles in periodic dynamical systems

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  • Irina Bashkirtseva

    (Ural Federal University)

Abstract

A non-linear dynamical system with periodic parameters is considered in presence of random noise. A dispersion of stochastic trajectories around the deterministic cycle is studied on the base of the stochastic sensitivity analysis. For weak noise, the asymptotics of this dispersion is found in a form of periodic matrix function named by the stochastic sensitivity matrix. This matrix is a solution of the boundary value problem for some matrix linear differential equation. A mathematical analysis of this problem is carried out, and an explicit solution is presented for one-dimensional case. The elaborated mathematical method is applied to the analysis of the stochastic population model with Allee effect and periodic modulation. A dependence of the stochastic sensitivity of oscillations on the amplitude and frequency of periodic forcing is investigated. A phenomenon of the noise-induced transition from persistence to extinction is studied by confidence domains constructed on the base of the stochastic sensitivity function technique.

Suggested Citation

  • Irina Bashkirtseva, 2018. "Stochastic sensitivity of cycles in periodic dynamical systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(11), pages 1-6, November.
    • Handle: RePEc:spr:eurphb:v:91:y:2018:i:11:d:10.1140_epjb_e2018-90152-3
    DOI: 10.1140/epjb/e2018-90152-3
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    Keywords

    Statistical and Nonlinear Physics;

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