TY - JOUR

T1 - Bifurcation structure of coexistence states for a prey-predator model with large population flux by attractive transition

AU - Kuto, Kousuke

AU - Oeda, Kazuhiro

N1 - Publisher Copyright:
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

PY - 2021

Y1 - 2021

N2 - This paper is concerned with a prey-predator model with population flux by attractive transition. Our previous paper (Oeda and Kuto, 2018, Nonlinear Anal. RWA, 44, 589-615) obtained a bifurcation branch (connected set) of coexistence steady states which connects two semitrivial solutions. In Oeda and Kuto (2018, Nonlinear Anal. RWA, 44, 589-615), we also showed that any positive steady-state approaches a positive solution of either of two limiting systems, and moreover, one of the limiting systems is an equal diffusive competition model. This paper obtains the bifurcation structure of positive solutions to the other limiting system. Moreover, this paper implies that the global bifurcation branch of coexistence states consists of two parts, one of which is a simple curve running in a tubular domain near the set of positive solutions to the equal diffusive competition model, the other of which is a connected set characterized by positive solutions to the other limiting system.

AB - This paper is concerned with a prey-predator model with population flux by attractive transition. Our previous paper (Oeda and Kuto, 2018, Nonlinear Anal. RWA, 44, 589-615) obtained a bifurcation branch (connected set) of coexistence steady states which connects two semitrivial solutions. In Oeda and Kuto (2018, Nonlinear Anal. RWA, 44, 589-615), we also showed that any positive steady-state approaches a positive solution of either of two limiting systems, and moreover, one of the limiting systems is an equal diffusive competition model. This paper obtains the bifurcation structure of positive solutions to the other limiting system. Moreover, this paper implies that the global bifurcation branch of coexistence states consists of two parts, one of which is a simple curve running in a tubular domain near the set of positive solutions to the equal diffusive competition model, the other of which is a connected set characterized by positive solutions to the other limiting system.

KW - Asymptotic behaviour

KW - attractive transitional flux

KW - bifurcation analysis

KW - coexistence steady states

KW - Lyapunov-Schmidt reduction

KW - prey-predator model

UR - http://www.scopus.com/inward/record.url?scp=85113520431&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85113520431&partnerID=8YFLogxK

U2 - 10.1017/prm.2021.43

DO - 10.1017/prm.2021.43

M3 - Article

AN - SCOPUS:85113520431

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

ER -