Bifurcation structure of stationary solutions for a chemotaxis system with bistable growth

Hirofumi Izuhara, Kousuke Kuto, Tohru Tsujikawa

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

From the viewpoint of pattern formation, Keller–Segel systems with growth terms are studied. These models exhibit various stationary and spatio-temporal patterns which are caused by a combination of three effects: chemotaxis, diffusion and growth. In this paper, we consider Keller–Segel system with the cubic growth term known as the Allee effect in ecology and its shadow system in the limiting case that the mobility of biological population tends to infinity. We show the existence and stability of stationary solutions of the shadow system in one space dimension. Our proof is based on the bifurcation theory, a singular perturbation method and a level set analysis. We also show some numerical results on global structures of stationary solutions in the systems by using AUTO package. Moreover, we mention the difference in dynamics between Keller–Segel system with the cubic growth term and that with the logistic growth term with the aid of a computer.

Original languageEnglish
Pages (from-to)441-475
Number of pages35
JournalJapan Journal of Industrial and Applied Mathematics
Volume35
Issue number2
DOIs
Publication statusPublished - 2018 Jul 1
Externally publishedYes

Fingerprint

Chemotaxis
Stationary Solutions
Bifurcation
Term
Logistic Growth
Allee Effect
Singular Perturbation Method
Ecology
Spatio-temporal Patterns
Bifurcation Theory
Logistics
Pattern Formation
Level Set
Limiting
Infinity
Tend
Numerical Results

Keywords

  • Bifurcation analysis
  • Keller–Segel system with growth
  • Pattern formation
  • Shadow system

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

Cite this

Bifurcation structure of stationary solutions for a chemotaxis system with bistable growth. / Izuhara, Hirofumi; Kuto, Kousuke; Tsujikawa, Tohru.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 35, No. 2, 01.07.2018, p. 441-475.

Research output: Contribution to journalArticle

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