Global asymptotic stability of a ratio-dependent predator-prey system with diffusion
type: Item
instance of: scholarly article
title: Global asymptotic stability of a ratio-dependent predator-prey system with diffusion
zbMATH Open document ID: 1093.35039
author: Yong-Hong Fan
author: Wan-Tong Li
published in: Journal of Computational and Applied Mathematics
publication date: 2006-03-16T00:00:00Z
review text: The authors investigate a predator-prey system with diffusion. The main attention is paid to the global asymptotic stability of the positive constant equilibrium of the system. In order to prove the main results, the authors consider the local asymptotic stability and then obtain some estimation of the solutions. The proof is completed by constructing Lyapunov functions, the method of upper and lower solutions combined with the monotone iteration.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5012886
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: positive constant equilibrium
zbMATH Keywords: monotone iteration
reviewed by: Sebastian Aniţa
MaRDI profile type: Publication
Wikidata QID: Q115581123
full work available at URL: j.cam.2005.04.007
OpenAlex ID: W2034616222
cites work: Q3262986
cites work: Global analyses in some delayed ratio-dependent predator-prey systems
cites work: Periodic solutions of delayed ratio-dependent predator--prey models with monotonic or nonmonotonic functional responses
cites work: Q3895297
cites work: Q4003237
cites work: Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system
cites work: Rich dynamics of a ratio-dependent one-prey two-predators model
cites work: About deterministic extinction in ratio-dependent predator-prey models
cites work: Delay differential equations: with applications in population dynamics
cites work: Global qualitative analysis of a ratio-dependent predator-prey system
cites work: Q3994920
cites work: Qualitative analysis of a ratio-dependent predator–prey system with diffusion
cites work: Strategy and stationary pattern in a three-species predator--prey model
cites work: Global analysis in a predator-prey system with nonmonotonic functional response
cites work: Q4883783
cites work: Existence and global stability of positive periodic solutions of a predator-prey system with delays
cites work: Periodic solutions and permanence for a delayed nonautonomous ratio-dependent predator-prey model with Holling type functional response.
cites work: Global dynamics of a ratio-dependent predator-prey system
cites work: On the uniqueness and nonexistence of limit cycles for predator prey systems
cites work: Bifurcation Analysis of a Predator-Prey System with Nonmonotonic Functional Response
DOI: 10.1016/J.CAM.2005.04.007
description: scientific article; zbMATH DE number 5012886