Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/43930
Title: Global bifurcation and stability of steady states for a reaction-diffusion-chemotaxis model with volume-filling effect
Authors: Ma, M
Wang, ZA 
Keywords: Bifurcation theory
Stability
Steady states
Issue Date: 2015
Publisher: Institute of Physics Publishing
Source: Nonlinearity, 2015, v. 28, no. 8, p. 2639-2660 How to cite?
Journal: Nonlinearity 
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.
URI: http://hdl.handle.net/10397/43930
ISSN: 0951-7715
DOI: 10.1088/0951-7715/28/8/2639
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