Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments
type: Item
instance of: scholarly article
title: Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments
zbMATH Open document ID: 1485.92088
author: Xin He
author: Xin Zhao
author: Tao Feng
author: Zhipeng Qiu
published in: Mathematica Slovaca
publication date: 2021-12-03T00:00:00Z
review text: In this paper, based on the deterministic prey-predator model owning foraging arena scheme, the authors have proposed a stochastic foraging arena prey-predator model in presence of environmental pollution. The sufficient criterions for uniform weak persistence in the mean and extinction have been obtained. The threshold between persistence and extinction has been also derived for the prey population. The authors have also showed the existence of a positive periodic solution under appropriate conditions. Finally, the authors present some numerical simulations to visually demonstrate their theoretical results. This paper is mostly inspired by the works of \textit{M. Liu} and \textit{K. Wang} [``Survival analysis of stochastic single-species population models in polluted environments'', Ecol. Model. 220, No. 9--10, 1347--1357 (2009; \url{doi:10.1016/j.ecolmodel.2009.03.001})].
reviewed by: Yingxin Guo
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7438337
zbMATH Keywords: stochastic prey-predator model
zbMATH Keywords: Brownian motion
zbMATH Keywords: extinction
zbMATH Keywords: environmental pollution
zbMATH Keywords: periodic solution
MaRDI profile type: Publication
full work available at URL: ms-2017-0463
OpenAlex ID: W3131633871
Wikidata QID: Q113236299
cites work: Model selection for integrated pest management with stochasticity
cites work: Stochastic prey-predator system with foraging arena scheme
cites work: Global analysis of a stochastic TB model with vaccination and treatment
cites work: Dynamics of a stochastic hepatitis C virus system with host immunity
cites work: Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation
cites work: Q3340544
cites work: Analysis of a delayed stochastic predator-prey model in a polluted environment
cites work: An algorithmic introduction to numerical simulation of stochastic differential equations
cites work: Dynamical behavior of a one predator and two independent preys system with stochastic perturbations
cites work: Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies
cites work: Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
cites work: Dynamics of a stochastic predator-prey model with stage structure for predator and Holling type II functional response
cites work: Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
cites work: Survival analysis of stochastic competitive models in a polluted environment and stochastic competitive exclusion principle
cites work: Asymptotic properties of a stochastic predator-prey system with Holling II functional response
cites work: Persistence and extinction of a population in a polluted environment
cites work: Q5429735
cites work: GLOBAL DYNAMICS ANALYSIS OF A NONLINEAR IMPULSIVE STOCHASTIC CHEMOSTAT SYSTEM IN A POLLUTED ENVIRONMENT
cites work: Coexistence and exclusion of stochastic competitive Lotka-Volterra models
cites work: Q3597003
cites work: Dynamics of a stochastic delayed Harrison-type predation model: effects of delay and stochastic components
DOI: 10.1515/MS-2017-0463
description: scientific article; zbMATH DE number 7438337