The One Dimensional Keller-Segel Model
Abstract
In this paper, the Keller-Segel model is analysed. The work presented will focus on the mass criticality results for the Chemotaxis model. Subsequently the relative stability of stationary states are analysed using the Keller-Segel system for the Chemotaxis with linear diffusion. In this analysis, the techniques of ‘separation of variables’ and ‘standard linearization’ were used. Also, the graphics illustrate stability or instability in all the cases analysed.
Keywords
References
- KELLER E.F. and SEGEL, L.A., (1970). Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol., (26), 399-415. KELLER E.F. and SEGEL, L.A., (1971). Model for Chemotaxis, J. Theor. Biol., (30), 225-234. HORSTMAN, D., (2001). Lyapunov functions and L p-estimates for a class of reaction diffusion system , Coll.math., (87), 113-127. MURRAY, J.D., (2002). Mathematical Biology I:an Introduction, 3rd. Edn., Interdisciplinary Applied Mathematics, (33), 405-406. HORSTMAN, D., (2003). From 1970 until present: the Keller-Segel model in Chemotaxis and its consequences, JI. Jahresberrichte DMV., (105), 103-165. PERTHAME, B., (2007). Transport Equations in Biology, Birkhauser., (48),28-31. HILLEN, T. and PAINTER, K.J., (2009). A user’s guide to PDE models for chemotaxis, Journal of Mathematical Biology., (58) 183-217.
Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Publication Date
April 30, 2017
Submission Date
May 10, 2017
Acceptance Date
March 25, 2017
Published in Issue
Year 2017 Volume: 3 Number: 1