Effect of cross-diffusion on the stationary problem of a prey-predator model with a protection zone

Kazuhiro Oeda

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

This paper is concerned with the stationary problem of a prey-predator cross-diffusion system with a protection zone for the prey. We discuss the existence and non-existence of coexistence states of the two species by using the bifurcation theory. As a result, it is shown that the cross-diffusion for the prey has beneficial effects on the survival of the prey when the intrinsic growth rate of the predator is positive. We also study the asymptotic behavior of positive stationary solutions as the cross-diffusion coefficient of the prey tends to infinity.

Original languageEnglish
Pages (from-to)3988-4009
Number of pages22
JournalJournal of Differential Equations
Volume250
Issue number10
DOIs
Publication statusPublished - 2011 May 15

Fingerprint

Prey-predator Model
Cross-diffusion
Prey
Cross-diffusion System
Coexistence States
Bifurcation Theory
Predator-prey System
Predator
Stationary Solutions
Diffusion Coefficient
Nonexistence
Asymptotic Behavior
Infinity
Tend

Keywords

  • Bifurcation
  • Cross-diffusion
  • Prey-predator model
  • Protection zone

ASJC Scopus subject areas

  • Analysis

Cite this

Effect of cross-diffusion on the stationary problem of a prey-predator model with a protection zone. / Oeda, Kazuhiro.

In: Journal of Differential Equations, Vol. 250, No. 10, 15.05.2011, p. 3988-4009.

Research output: Contribution to journalArticle

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