Loading...
Pattern Formation of the Attraction-Repulsion Keller-Segel System
Liu, Ping Shi, Junping Wang, Zhi-An
Liu, Ping
Shi, Junping
Wang, Zhi-An
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).
Description
Date
2012-12-31
Journal Title
Journal ISSN
Volume Title
Publisher
Collections
Download Dataset
Rights Holder
Usage License
Embargo
Research Projects
Organizational Units
Journal Issue
Keywords
Citation
Advisor
Department
Mathematics
DOI
10.3934/dcdsb.2013.18.2597