Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics

Hitoshi Ishii, Izumi Takagi

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

We consider a nonlinear diffusion equation proposed by Shigesada and Okubo which describes phytoplankton growth dynamics with a selfs-hading effect. We show that the following alternative holds: Either (i) the trivial stationary solution which vanishes everywhere is a unique stationary solution and is globally stable, or (ii) the trivial solution is unstable and there exists a unique positive stationary solution which is globally stable. A criterion for the existence of positive stationary solutions is stated in terms of three parameters included in the equation.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalJournal of Mathematical Biology
Volume16
Issue number1
DOIs
Publication statusPublished - 1982 Dec
Externally publishedYes

Fingerprint

Phytoplankton
Nonlinear Diffusion Equation
Global Stability
Stationary Solutions
phytoplankton
Growth
Trivial
Vanish
Unstable
Alternatives

Keywords

  • Global stability
  • Nonlinear diffusion equation
  • Self-shading

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Agricultural and Biological Sciences (miscellaneous)

Cite this

Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics. / Ishii, Hitoshi; Takagi, Izumi.

In: Journal of Mathematical Biology, Vol. 16, No. 1, 12.1982, p. 1-24.

Research output: Contribution to journalArticle

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