Izv. IMI UdGU, 2019, Volume 53, Pages 36–47
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,
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.
piecewise-smooth map, population dynamics, stochastic sensitivity.
|Russian Science Foundation
|The research was supported by the Russian Science Foundation (project no. 16-11-10098).
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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
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\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
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