Pattern Formation of the Attraction-Repulsion Keller-Segel System
By Ping Liu, Junping Shi, Zhian Wang. 2013
163 citations recorded by the source corpus.
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).
Subfields: Cell Biology, Modeling and Simulation, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/f93d4f8bf2b30536e4547079ccfe7c6eefed37b5
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In Cell Biology
In Modeling and Simulation
In Molecular Biology
Citations in the corpus
- Boundedness of the attraction–repulsion Keller–Segel system (2015, methodology): “Furthermore the time-periodic orbits have been found recently in [16] by employing the local and global Hopf bifurcation theory.”