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Izv. IMI UdGU, 2019, Volume 53, Pages 36–47 (Mi iimi369)  

The stochastic sensitivity function method in analysis of the piecewise-smooth model of population dynamics

A. V. Belyaev, T. V. Ryazanova

Ural Federal University, pr. Lenina, 51, Yekaterinburg, 620000, Russia

Abstract: This work is devoted to the application of the stochastic sensitivity function method to attractors of a piecewise-smooth one-dimensional map describing the dynamics of the population size. The first stage of the study is a parametric analysis of possible modes of the deterministic model: the definition of zones of existence of stable equilibria and chaotic attractors. The theory of critical points is used to determine the parametric boundaries of a chaotic attractor. In the case where the system is influenced by a random effect, based on the technique of the stochastic sensitivity function, a description of the spread of random states around the equilibrium and chaotic attractor is carried out. A comparative analysis of the influence of parametric and additive noise on the attractors of the system is conducted. Using the technique of confidence intervals, probabilistic mechanisms of extinction of a population under the influence of random disturbances are studied. Changes in the parametric boundaries of the existence of a population under the impact of a random perturbation are analyzed.

Keywords: piecewise-smooth map, population dynamics, stochastic sensitivity.

Funding Agency Grant Number
Russian Science Foundation 16-11-10098
The research was supported by the Russian Science Foundation (project no. 16-11-10098).


DOI: https://doi.org/10.20537/2226-3594-2019-53-04

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UDC: 519.21
MSC: 39A50
Received: 04.04.2019

Citation: A. V. Belyaev, T. V. Ryazanova, “The stochastic sensitivity function method in analysis of the piecewise-smooth model of population dynamics”, Izv. IMI UdGU, 53 (2019), 36–47

Citation in format AMSBIB
\Bibitem{BelRya19}
\by A.~V.~Belyaev, T.~V.~Ryazanova
\paper The stochastic sensitivity function method in analysis of the piecewise-smooth model of population dynamics
\jour Izv. IMI UdGU
\yr 2019
\vol 53
\pages 36--47
\mathnet{http://mi.mathnet.ru/iimi369}
\crossref{https://doi.org/10.20537/2226-3594-2019-53-04}
\elib{http://elibrary.ru/item.asp?id=38503197}


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