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 Izv. IMI UdGU, 2019, Volume 53, Pages 3–14 (Mi iimi366)

Analysis of the influence of parametric noise on the dynamics of two interacting populations

E. P. Abramova, T. V. Ryazanova

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

Abstract: This paper considers the predator-prey population model, which combines both the stabilizing factors of the intraspecific competition of prey and predator (for resources other than the prey), and the predator saturation. The purpose of this study is a comparative parametric analysis of stochastic phenomena which occur under parametric noise of two different types. The stochastic sensitivity of the attractors is studied. Based on the stochastic sensitivity function technique, noise-induced phenomena are described. In the parametric bistable zone, transitions of two types are carried out: equilibrium $\rightarrow$ equilibrium and cycle $\rightarrow$ equilibrium. The values of critical intensities for the occurrence of transition phenomena between attractors are obtained. In the parametric monostable zone, such phenomena as cycle deformation and equilibrium shift are demonstrated.

Keywords: population model, parametric noise, noise-induced phenomena.

 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/10.20537/2226-3594-2019-53-01

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UDC: 519.21
MSC: 39A50

Citation: E. P. Abramova, T. V. Ryazanova, “Analysis of the influence of parametric noise on the dynamics of two interacting populations”, Izv. IMI UdGU, 53 (2019), 3–14

Citation in format AMSBIB
\Bibitem{AbrRya19} \by E.~P.~Abramova, T.~V.~Ryazanova \paper Analysis of the influence of parametric noise on the dynamics of two interacting populations \jour Izv. IMI UdGU \yr 2019 \vol 53 \pages 3--14 \mathnet{http://mi.mathnet.ru/iimi366} \crossref{https://doi.org/10.20537/2226-3594-2019-53-01} \elib{http://elibrary.ru/item.asp?id=38503194}