Steady-state solutions of a diffusive prey-predator model with finitely many protection zones

Kazuhiro Oeda

Research output: Contribution to journalArticle

Abstract

This paper is concerned with a diffusive Lotka-Volterra prey-predator model with finitely many protection zones for the prey species. We discuss the stability of trivial and semi-trivial steady-state solutions, and we also study the existence and non-existence of positive steady-state solutions. It is proved that there exists a certain critical growth rate of the prey for survival. Moreover, it is shown that when cross-diffusion is present, under certain conditions, the critical value decreases as the number of protection zones increases. On the other hand, it is also shown that when cross-diffusion is absent, the critical value does not always decrease even if the number of protection zones increases.

Original languageEnglish
Pages (from-to)19-38
Number of pages20
JournalSUT Journal of Mathematics
Volume53
Issue number1
Publication statusPublished - 2017 Jan 1

Fingerprint

Prey-predator Model
Steady-state Solution
Cross-diffusion
Prey
Critical value
Trivial
Critical Growth
Decrease
Lotka-Volterra Model
Nonexistence

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Steady-state solutions of a diffusive prey-predator model with finitely many protection zones. / Oeda, Kazuhiro.

In: SUT Journal of Mathematics, Vol. 53, No. 1, 01.01.2017, p. 19-38.

Research output: Contribution to journalArticle

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