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The One Dimensional Keller-Segel Model

Year 2017, Volume: 3 Issue: 1, 38 - 41, 30.04.2017

Mustafa Ali Dokuyucu Ercan Çelik

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

Chemotaxis Keller-Segel Model

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.

Year 2017, Volume: 3 Issue: 1, 38 - 41, 30.04.2017

Mustafa Ali Dokuyucu Ercan Çelik

Abstract

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.
There are 1 citations in total.

Details

Journal Section Volume 3 Issue 1
Authors

Mustafa Ali Dokuyucu

Ercan Çelik

Publication Date April 30, 2017
Published in Issue Year 2017 Volume: 3 Issue: 1

Cite

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. April 2017;3(1):38-41.
Chicago Dokuyucu, Mustafa Ali, and Ercan Çelik. “The One Dimensional Keller-Segel Model”. Eastern Anatolian Journal of Science 3, no. 1 (April 2017): 38-41.
EndNote Dokuyucu MA, Çelik E (April 1, 2017) The One Dimensional Keller-Segel Model. Eastern Anatolian Journal of Science 3 1 38–41.
IEEE M. A. Dokuyucu and E. Çelik, “The One Dimensional Keller-Segel Model”, Eastern Anatolian Journal of Science, vol. 3, no. 1, pp. 38–41, 2017.
ISNAD Dokuyucu, Mustafa Ali - Çelik, Ercan. “The One Dimensional Keller-Segel Model”. Eastern Anatolian Journal of Science 3/1 (April 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 and Ercan Çelik. “The One Dimensional Keller-Segel Model”. Eastern Anatolian Journal of Science, vol. 3, no. 1, 2017, pp. 38-41.
Vancouver Dokuyucu MA, Çelik E. The One Dimensional Keller-Segel Model. Eastern Anatolian Journal of Science. 2017;3(1):38-41.