Global bifurcation and stability of steady states for a reaction-diffusion-chemotaxis model with volume-filling effect

Manjun Ma, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)

Abstract

This paper is devoted to studying a reaction-diffusion-chemotaxis model with a volume-filling effect in a bounded domain with Neumann boundary conditions. We first establish the global existence of classical solutions bounded uniformly in time. Then applying the asymptotic analysis and bifurcation theory, we obtain both the local and global structure of steady states bifurcating from the homogeneous steady states in one dimension by treating the chemotactic coefficient as a bifurcation parameter. Moveover we find the stability criterion of the bifurcating steady states and give a sufficient condition for the stability of steady states with small amplitude. The pattern formation of the model is numerically shown and the stability criterion is verified by our numerical simulations.
Original languageEnglish
Pages (from-to)2639-2660
Number of pages22
JournalNonlinearity
Volume28
Issue number8
DOIs
Publication statusPublished - 29 Jun 2015

Keywords

  • bifurcation theory
  • stability
  • steady states

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this