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

Kousuke Kuto, Kazuhiro Oeda

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Asymptotic behaviour
  • attractive transitional flux
  • bifurcation analysis
  • coexistence steady states
  • Lyapunov-Schmidt reduction
  • prey-predator model

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'Bifurcation structure of coexistence states for a prey-predator model with large population flux by attractive transition'. Together they form a unique fingerprint.

Cite this