Stability of steady-state solutions to a prey-predator system with cross-diffusion

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Abstract

This paper is concerned with a cross-diffusion system arising in a prey-predator population model. The main purpose is to discuss the stability analysis for coexistence steady-state solutions obtained by Kuto and Yamada (J. Differential Equations, to appear). We will give some criteria on the stability of these coexistence steady states. Furthermore, we show that the Hopf bifurcation phenomenon occurs on the steady-state solution branch under some conditions.

Original languageEnglish
Pages (from-to)293-314
Number of pages22
JournalJournal of Differential Equations
Volume197
Issue number2
DOIs
Publication statusPublished - 2004 Mar 1

Keywords

  • Cross diffusion
  • Hopf bifurcation
  • Lyapunov-Schmidt reduction
  • Stability
  • Steady-state solution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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