Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/21797
Title: Pattern formation of the attraction-repulsion keller-segel system
Authors: Liu, P
Shi, J
Wang, ZA 
Keywords: Attraction-repulsion chemotaxis
Hopf bifurcation
Steady state bifurcation
Time-periodic patterns.
Issue Date: 2013
Publisher: Amer Inst Mathematical Sciences
Source: Discrete and continuous dynamical systems - series b, 2013, v. 18, no. 10, p. 2597-2625 How to cite?
Journal: Discrete and Continuous Dynamical Systems - Series B 
Abstract: In this paper the pattern formation of the attraction-repulsion Keller-Segel (ARKS) system is studied analytically and numerically By the Hopf bifurcation theorem as well as the local and global bifurcation theorem we rigorously establish the existence of time-periodic patterns and steady state patterns for the ARKS model in the full parameter regimes which are identified by a linear stability analysis We also show that when the chemotactic attraction is strong a spiky steady state pattern can develop Explicit time-periodic rippling wave patterns and spiky steady state patterns are obtained numerically by carefully selecting parameter values based on our theoretical results The study in the paper asserts that chemotactic competitive interaction between attraction and repulsion can produce periodic patterns which are impossible for the chemotaxis model with a single chemical (either chemo-attractant or chemo-repellent).
URI: http://hdl.handle.net/10397/21797
ISSN: 1531-3492
DOI: 10.3934/dcdsb.2013.18.2597
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