Stochastic sensitivity of cycles in periodic dynamical systems

  • Irina BashkirtsevaEmail author
Regular Article


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.


Statistical and Nonlinear Physics 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Ural Federal UniversityEkaterinburgRussia

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