Existence, extinction and global asymptotical stability of a stochastic predator-prey model with mutual interference
type: Item
instance of: scholarly article
title: Existence, extinction and global asymptotical stability of a stochastic predator-prey model with mutual interference
zbMATH Open document ID: 1315.34062
author: Bo Du
published in: Journal of Applied Mathematics and Computing
publication date: 2014-09-12T00:00:00Z
review text: The author considers a stochastic predator-pray model with mutual interference and stochastic growth rates. Sufficient criteria for the global asymptotic stability are established. Results are illustrated by computer simulation by means of the Milshtein numerical method. The author considers a linear Volterra difference equation in a Banach space. The obtained results on asymptotic stability and almost periodicity are stated in terms of spectral properties of the equation. Spectral theory of unilateral sequences is applied.
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 6343563
zbMATH Keywords: stochastic perturbations
zbMATH Keywords: global stability
zbMATH Keywords: mutual interference
reviewed by: Alexandra Rodkina
MaRDI profile type: Publication
full work available at URL: s12190-013-0738-1
OpenAlex ID: W2076458204
Wikidata QID: Q115601678
cites work: On the Nonautonomous Volterra-Lotka Competition Equations
cites work: Existence and global attractivity of positive periodic solutions to periodic \(n\)-species Lotka-Volterra competition systems with several deviating arguments
cites work: Q4366367
cites work: Q4652189
cites work: Existence and global asymptotic stability of positive periodic solution for a predator-prey system with mutual interference
cites work: Global attractivity of positive periodic solution for a Volterra model
cites work: Permanence and global asymptotical stability of a predator-prey model with mutual interference
cites work: Permanence of a discrete periodic Volterra model with mutual interference
cites work: Almost periodic solution for a Volterra model with mutual interference and Beddington-DeAngelis functional response
cites work: Existence and global attractivity of positive periodic solution to a Lotka-Volterra model
cites work: Persistence in stochastic food web models
cites work: Q3764976
cites work: Ratio-dependent predator–prey model: effect of environmental fluctuation and stability
cites work: Q4429919
cites work: Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
cites work: Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment
cites work: Population dynamical behavior of Lotka-Volterra cooperative systems with random perturbations
cites work: Long-time behaviour of a stochastic prey--predator model.
cites work: Dynamics of a two-prey one-predator system in random environments
cites work: Q3959169
cites work: Q4002114
cites work: Q3262986
cites work: An algorithmic introduction to numerical simulation of stochastic differential equations
DOI: 10.1007/S12190-013-0738-1
Recommended article: Dynamics of a stochastic predator-prey model with mutual interference
Recommended article: Global dynamics of stochastic predator-prey model with mutual interference and prey defense
Recommended article: Permanence and global asymptotical stability of a predator-prey model with mutual interference
Recommended article: Q4623823
Recommended article: Persistence, extinction and global asymptotical stability of a non-autonomous predator-prey model with random perturbation
Recommended article: On the asymptotic stability of an Hassell predator-prey model with mutual interference
Recommended article: Global stability of a stage-structured predator-prey model with stochastic perturbation
Recommended article: Existence and global asymptotic stability of positive periodic solution for a predator-prey system with mutual interference
Recommended article: Q2948852
Recommended article: Existence, stationary distribution, and extinction of predator-prey system of prey dispersal with stochastic perturbation
description: scientific article; zbMATH DE number 6343563