Positive steady states for a prey–predator model with population flux by attractive transition

Kazuhiro Oeda, Kousuke Kuto

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper studies the stationary solutions of a prey–predator model with population flux by attractive transition. We first obtain a bifurcation branch (connected set) of positive solutions which connects two semitrivial solutions. Next we derive the asymptotic behavior of positive solutions as the coefficient α of the population flux tends to infinity. A main result implies that positive solutions can be classified into two types as α→∞. In one type of them, as α→∞, positive solutions of the prey–predator model approach positive solutions of a competition model with equal diffusion coefficients.

Original languageEnglish
Pages (from-to)589-615
Number of pages27
JournalNonlinear Analysis: Real World Applications
Volume44
DOIs
Publication statusPublished - 2018 Dec 1
Externally publishedYes

Fingerprint

Prey-predator Model
Positive Solution
Fluxes
Competition Model
Connected Set
Stationary Solutions
Diffusion Coefficient
Branch
Bifurcation
Asymptotic Behavior
Infinity
Tend
Imply
Coefficient
Coefficients

Keywords

  • A priori estimate
  • Asymptotic behavior
  • Attractive transitional flux
  • Bifurcation analysis
  • Coexistence steady states
  • Prey–predator model

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

Cite this

Positive steady states for a prey–predator model with population flux by attractive transition. / Oeda, Kazuhiro; Kuto, Kousuke.

In: Nonlinear Analysis: Real World Applications, Vol. 44, 01.12.2018, p. 589-615.

Research output: Contribution to journalArticle

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