Global stability and periodic orbits for two-patch predator-prey diffusion-delay models
type: Item
instance of: scholarly article
title: Global stability and periodic orbits for two-patch predator-prey diffusion-delay models
zbMATH Open document ID: 0634.92017
DOI: 10.1016/0025-5564(87)90051-4
author: Fortunata Solimano
author: Yasuhiro Takeuchi
author: E. Beretta
published in: Mathematical Biosciences
publication date: 1987-01-01T00:00:00Z
review text: A mathematical model for a one-prey, one-predator system in which the prey can diffuse between one patch with little food and no predation and one patch with much food but with predation is investigated. After transforming the corresponding system of integrodifferential equations into a system of ordinary differential equations, sufficient conditions for the boundedness of solutions and existence of a nonzero globally stable equilibrium are derived. Moreover, it is shown that a Hopf bifurcation may occur if the predator is not self-regulating.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D99
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 4033567
zbMATH Keywords: global stability
zbMATH Keywords: periodic orbits
zbMATH Keywords: two-patch predator-prey diffusion- delay models
zbMATH Keywords: Volterra within-patch dynamics
zbMATH Keywords: exponential-decay memory function
zbMATH Keywords: homotopy techniques
zbMATH Keywords: self-regulating coefficient of predator
zbMATH Keywords: integrodifferential equations
zbMATH Keywords: sufficient conditions for the boundedness of solutions
zbMATH Keywords: existence of a nonzero globally stable equilibrium
zbMATH Keywords: Hopf bifurcation
reviewed by: Reinhard Bürger
MaRDI profile type: Publication
full work available at URL: 0025-5564(87)90051-4
OpenAlex ID: W2063775986
Wikidata QID: Q115599891
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description: scientific article; zbMATH DE number 4033567