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

Hitoshi Ishii, Izumi Takagi

研究成果: Article

33 引用 (Scopus)

抄録

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.

元の言語English
ページ(範囲)1-24
ページ数24
ジャーナルJournal of Mathematical Biology
16
発行部数1
DOI
出版物ステータスPublished - 1982 12
外部発表Yes

Fingerprint

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

ASJC Scopus subject areas

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

これを引用

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

:: Journal of Mathematical Biology, 巻 16, 番号 1, 12.1982, p. 1-24.

研究成果: Article

@article{b104433313a549f8aa7e062219e2f3c9,
title = "Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics",
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.",
keywords = "Global stability, Nonlinear diffusion equation, Self-shading",
author = "Hitoshi Ishii and Izumi Takagi",
year = "1982",
month = "12",
doi = "10.1007/BF00275157",
language = "English",
volume = "16",
pages = "1--24",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Verlag",
number = "1",

}

TY - JOUR

T1 - Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics

AU - Ishii, Hitoshi

AU - Takagi, Izumi

PY - 1982/12

Y1 - 1982/12

N2 - 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.

AB - 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.

KW - Global stability

KW - Nonlinear diffusion equation

KW - Self-shading

UR - http://www.scopus.com/inward/record.url?scp=0020464810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020464810&partnerID=8YFLogxK

U2 - 10.1007/BF00275157

DO - 10.1007/BF00275157

M3 - Article

AN - SCOPUS:0020464810

VL - 16

SP - 1

EP - 24

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 1

ER -