Global attractivity of an integrodifferential model of mutualism
type: Item
instance of: scholarly article
title: Global attractivity of an integrodifferential model of mutualism
zbMATH Open document ID: 1474.34524
DOI: 10.1155/2014/928726
author: Xiangdong Xie
author: Fengde Chen
author: Kun Yang
author: Yalong Xue
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Sufficient conditions are obtained for the global attractivity of the following integrodifferential model of mutualism: \(d N_1(t) / d t = r_1 N_1(t) [((K_1 + \alpha_1 \int_0^{\infty} J_2(s) N_2(t - s) d s)/(1 + \int_0^{\infty} J_2(s) N_2(t - s) d s))- N_1(t)]\), \(d N_2(t) / d t = r_2 N_2(t) [((K_2 + \alpha_2 \int_0^{\infty} J_1(s) N_1(t - s) d s)/(1 + \int_0^{\infty} J_1(s) N_1(t - s) d s- N_2(t)]\), where \(r_i, K_i\), and \(\alpha_i\), \(i = 1,2\), are all positive constants. Consider \(\alpha_i > K_i\), \(i = 1,2 \). Consider \(\mathrm{J}_i \in C([0, + \infty)\), \([0, + \infty))\) and \(\int_0^{\infty} \mathrm{J}_i(s) d s = 1\), \(i = 1,2 \). Our result shows that conditions which ensure the permanence of the system are enough to ensure the global stability of the system. The result not only improves but also complements some existing ones.
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 7023330
Wikidata QID: Q59042900
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/928726
OpenAlex ID: W2112121588
cites work: The effect of delays on the permanence for Lotka-Volterra systems
cites work: Persistence, attractivity, and delay in facultative mutualism
cites work: Permanence and global attractivity for facultative mutualism system with delay
cites work: Delay effect on the permanence for Lotka-Volterra cooperative systems
cites work: Permanence for two-species Lotka-Volterra cooperative systems with delays
cites work: Permanence for nonautonomous Lotka-Volterra cooperative systems with delays
cites work: On the stable periodic solutions of a delayed two-species model of facultative mutualism
cites work: On the existence of positive periodic solutions to a Lotka-Volterra cooperative population model with multiple delays
cites work: Q4003237
cites work: Positive periodic solutions for an integrodifferential model of mutualism
cites work: Permanence for an integrodifferential model of mutualism
cites work: The dynamic behavior of \(N\)-species cooperation system with continuous time delays and feedback controls
cites work: Theory of functional differential equations. 2nd ed
cites work: Extinction in a two dimensional Lotka-Volterra system with infinite delay
cites work: On a mutualism model with feedback controls
cites work: Permanence of a delayed discrete mutualism model with feedback controls
cites work: Permanence of an \(N\)-species cooperation system with continuous time delays and feedback controls
cites work: Permanence of a discrete \(n\)-species cooperation system with time-varying delays and feedback controls
cites work: On a nonlinear nonautonomous predator--prey model with diffusion and distributed delay
Recommended article: Global attractivity in a discrete mutualism model with infinite deviating arguments
Recommended article: Global attractivity of a periodic delayed \(N\)-species model of facultative mutualism
Recommended article: Global and blow-up solutions for a mutualistic model
Recommended article: Global attractivity of an integro-differential model of competition
Recommended article: Global attractivity of a generalized Lotka-Volterra competition model
Recommended article: Global attractivity in an almost periodic multi-species nonlinear ecological model
Recommended article: Global stability of a discrete mutualism model
Recommended article: Q3179960
Recommended article: Q5260454
Recommended article: Global attractivity and almost periodic solution of a discrete mutualism model with delays
description: scientific article; zbMATH DE number 7023330