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

Kazuhiro Oeda; Kousuke Kuto

doi:10.1016/j.nonrwa.2018.06.006

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

Kazuhiro Oeda, Kousuke Kuto

Research output: Contribution to journal › Article › peer-review

2 Citations (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 language	English
Pages (from-to)	589-615
Number of pages	27
Journal	Nonlinear Analysis: Real World Applications
Volume	44
DOIs	https://doi.org/10.1016/j.nonrwa.2018.06.006
Publication status	Published - 2018 Dec
Externally published	Yes

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

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title = "Positive steady states for a prey–predator model with population flux by attractive transition",

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.",

keywords = "A priori estimate, Asymptotic behavior, Attractive transitional flux, Bifurcation analysis, Coexistence steady states, Prey–predator model",

author = "Kazuhiro Oeda and Kousuke Kuto",

note = "Funding Information: The authors would like to thank the referees for their many valuable comments and useful suggestions which helped improve the exposition of the current paper. The first author was supported by a Waseda University Grant for Special Research Projects (Grant Number 2016K-360 ). The second author was supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (C), Grant Number 15K04948 . ",

year = "2018",

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doi = "10.1016/j.nonrwa.2018.06.006",

language = "English",

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journal = "Nonlinear Analysis: Real World Applications",

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T1 - Positive steady states for a prey–predator model with population flux by attractive transition

AU - Oeda, Kazuhiro

AU - Kuto, Kousuke

N1 - Funding Information: The authors would like to thank the referees for their many valuable comments and useful suggestions which helped improve the exposition of the current paper. The first author was supported by a Waseda University Grant for Special Research Projects (Grant Number 2016K-360 ). The second author was supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (C), Grant Number 15K04948 .

PY - 2018/12

Y1 - 2018/12

N2 - 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.

AB - 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.

KW - A priori estimate

KW - Asymptotic behavior

KW - Attractive transitional flux

KW - Bifurcation analysis

KW - Coexistence steady states

KW - Prey–predator model

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