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.
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
\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{https://elibrary.ru/item.asp?id=38503197}
Linking options:
https://www.mathnet.ru/eng/iimi369
https://www.mathnet.ru/eng/iimi/v53/p36
This publication is cited in the following 2 articles:
A. V. Belyaev, T. V. Perevalova, “Stokhasticheskaya chuvstvitelnost kvaziperiodicheskikh i khaoticheskikh attraktorov diskretnoi modeli Lotki–Volterry”, Izv. IMI UdGU, 55 (2020), 19–32
A. V. Belyaev, T. V. Ryazanova, Springer Proceedings in Mathematics & Statistics, 318, Mathematical Analysis With Applications, 2020, 183
Citation in format AMSBIB
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