Geodesic
The stochastic sensitivity function method in analysis of the piecewise-smooth model of population dynamics
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 53 (2019), pp. 36-47

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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. 
@article{IIMI_2019_53_a3,
     author = {A. V. Belyaev and T. V. Ryazanova},
     title = {The stochastic sensitivity function method in analysis of the piecewise-smooth model of population dynamics},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {36--47},
     publisher = {mathdoc},
     volume = {53},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2019_53_a3/}
}
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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. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 53 (2019), pp. 36-47. http://geodesic.mathdoc.fr/item/IIMI_2019_53_a3/