Nonlinear diffusion for chemotaxis and birth-death process for Keller-Segel model

Yıl 2016, Cilt: 4 Sayı: 3, 204 - 211, 30.09.2016

Mustafa Ali Dokuyucu , Ercan Celik

Öz

This paper seeks to establish the stability of the
birth-death process in relation to the Keller-Segel Model. As well, it attempts
to describe the stability of non-linear diffusion for chemotaxis. Attention
will be on mass criticality results applying to the chemotaxis model.
Afterwards, the analysis of the relative stability that stationary states
exhibit is undertaken using the Keller-Segel system for the chemotaxis having
linear diffusion. Standard linearization and separation of variables are the
techniques employed in the analysis. The stability or instability of the
analysed cases is demonstrated by the graphics. By using the critical results
obtained for the models, the graphics are then compared with the rest.

Anahtar Kelimeler

Chemotaxis, Keller-Segel model

Kaynakça

• J.D. Murray, Mathematical Biology I: an Introduction, 3rd. edn., Interdisciplinary Applied Mathematics,17 405-406,(2002)
• T. Hofer, Chemotaxis and aggregation in the cellular slime mould, Berlin, 137-150,(1999)
• D. Horstman, From 1970 until present: the Keller-Segel model in chemotaxis and its consequences, I. Jahresberichte DMV. 105(3), 103-165,(2003)
• D. Horstman, Lyapunov functions and L p-estimates for a class of reaction diffusion systems, Coll. Math. 87,113-127,(2001)
• B. Perthame, Transport Equations in Biology, Birkhauser, (2007).
• T. Hillen and K.J. Painter, A user’s guide to PDE models for chemotaxis. Journal of Mathematical Biology, 58,183-217,(2009)
• E.F. Keller and L.A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol. 26,399-415,(1970)
• E.F. Keller and L.A. Segel, Model for chemotaxis, J. Theor. Biol. 30,225-234,(1971).
• M. R. Myerscough, P. K. Maini, J.D. Murray and K. H. Winters, Two dimensional pattern formation in a Chemotaxis system, In dynamics of complex interconnected biological system, 65-83, (1990).