Effect of cross-diffusion on the stationary problem of a prey-predator model with a protection zone

Kazuhiro Oeda

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38 Citations (Scopus)


This paper is concerned with the stationary problem of a prey-predator cross-diffusion system with a protection zone for the prey. We discuss the existence and non-existence of coexistence states of the two species by using the bifurcation theory. As a result, it is shown that the cross-diffusion for the prey has beneficial effects on the survival of the prey when the intrinsic growth rate of the predator is positive. We also study the asymptotic behavior of positive stationary solutions as the cross-diffusion coefficient of the prey tends to infinity.

Original languageEnglish
Pages (from-to)3988-4009
Number of pages22
JournalJournal of Differential Equations
Issue number10
Publication statusPublished - 2011 May 15



  • Bifurcation
  • Cross-diffusion
  • Prey-predator model
  • Protection zone

ASJC Scopus subject areas

  • Analysis

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