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2018 The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator
Jevgeņijs Carkovs, Jolanta Goldšteine, Kārlis Šadurskis
J. Appl. Math. 2018: 1-10 (2018). DOI: 10.1155/2018/6146027

Abstract

We present the analysis of a mathematical model of the dynamics of interacting predator and prey populations with the Holling type random trophic function under the assumption of random time interval passage between predator attacks on prey. We propose a stochastic approximation algorithm for quantitative analysis of the above model based on the probabilistic limit theorem. If the predators’ gains and the time intervals between predator attacks are sufficiently small, our proposed method allows us to derive an approximative average dynamical system for mathematical expectations of population dynamics and the stochastic Ito differential equation for the random deviations from the average motion. Assuming that the averaged dynamical system is the classic Holling type II population model with asymptotically stable limit cycle, we prove that the dynamics of stochastic model may be approximated with a two-dimensional Gaussian Markov process with unboundedly increasing variances.

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Jevgeņijs Carkovs. Jolanta Goldšteine. Kārlis Šadurskis. "The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator." J. Appl. Math. 2018 1 - 10, 2018. https://doi.org/10.1155/2018/6146027

Information

Received: 8 October 2017; Accepted: 23 January 2018; Published: 2018
First available in Project Euclid: 11 July 2018

zbMATH: 07132104
MathSciNet: MR3820027
Digital Object Identifier: 10.1155/2018/6146027

Rights: Copyright © 2018 Hindawi

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