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The One Dimensional Keller-Segel Model

Yıl 2017, Cilt: 3 Sayı: 1, 38 - 41, 30.04.2017

Mustafa Ali Dokuyucu Ercan Çelik

Öz

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.

Anahtar Kelimeler

Chemotaxis Keller-Segel Model

Kaynakça

  • 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.

Yıl 2017, Cilt: 3 Sayı: 1, 38 - 41, 30.04.2017

Mustafa Ali Dokuyucu Ercan Çelik

Öz

Kaynakça

  • 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.
Toplam 1 adet kaynakça vardır.

Ayrıntılar

Bölüm Volume 3 Issue 1
Yazarlar

Mustafa Ali Dokuyucu

Ercan Çelik

Yayımlanma Tarihi 30 Nisan 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 3 Sayı: 1

Kaynak Göster

APA Dokuyucu, M. A., & Çelik, E. (2017). The One Dimensional Keller-Segel Model. Eastern Anatolian Journal of Science, 3(1), 38-41.
AMA Dokuyucu MA, Çelik E. The One Dimensional Keller-Segel Model. Eastern Anatolian Journal of Science. Nisan 2017;3(1):38-41.
Chicago Dokuyucu, Mustafa Ali, ve Ercan Çelik. “The One Dimensional Keller-Segel Model”. Eastern Anatolian Journal of Science 3, sy. 1 (Nisan 2017): 38-41.
EndNote Dokuyucu MA, Çelik E (01 Nisan 2017) The One Dimensional Keller-Segel Model. Eastern Anatolian Journal of Science 3 1 38–41.
IEEE M. A. Dokuyucu ve E. Çelik, “The One Dimensional Keller-Segel Model”, Eastern Anatolian Journal of Science, c. 3, sy. 1, ss. 38–41, 2017.
ISNAD Dokuyucu, Mustafa Ali - Çelik, Ercan. “The One Dimensional Keller-Segel Model”. Eastern Anatolian Journal of Science 3/1 (Nisan 2017), 38-41.
JAMA Dokuyucu MA, Çelik E. The One Dimensional Keller-Segel Model. Eastern Anatolian Journal of Science. 2017;3:38–41.
MLA Dokuyucu, Mustafa Ali ve Ercan Çelik. “The One Dimensional Keller-Segel Model”. Eastern Anatolian Journal of Science, c. 3, sy. 1, 2017, ss. 38-41.
Vancouver Dokuyucu MA, Çelik E. The One Dimensional Keller-Segel Model. Eastern Anatolian Journal of Science. 2017;3(1):38-41.