Research Article
BibTex RIS Cite

The One Dimensional Keller-Segel Model

Year 2017, Volume: 3 Issue: 1, 38 - 41, 30.04.2017
https://izlik.org/JA84BF37WZ

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.

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
https://izlik.org/JA84BF37WZ

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 Research Article
Authors

Mustafa Ali Dokuyucu

Ercan Çelik

Publication Date April 30, 2017
IZ https://izlik.org/JA84BF37WZ
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. https://izlik.org/JA84BF37WZ
AMA 1.Dokuyucu MA, Çelik E. The One Dimensional Keller-Segel Model. Eastern Anatolian Journal of Science. 2017;3(1):38-41. https://izlik.org/JA84BF37WZ
Chicago Dokuyucu, Mustafa Ali, and Ercan Çelik. 2017. “The One Dimensional Keller-Segel Model”. Eastern Anatolian Journal of Science 3 (1): 38-41. https://izlik.org/JA84BF37WZ.
EndNote Dokuyucu MA, Çelik E (April 1, 2017) The One Dimensional Keller-Segel Model. Eastern Anatolian Journal of Science 3 1 38–41.
IEEE [1]M. A. Dokuyucu and E. Çelik, “The One Dimensional Keller-Segel Model”, Eastern Anatolian Journal of Science, vol. 3, no. 1, pp. 38–41, Apr. 2017, [Online]. Available: https://izlik.org/JA84BF37WZ
ISNAD Dokuyucu, Mustafa Ali - Çelik, Ercan. “The One Dimensional Keller-Segel Model”. Eastern Anatolian Journal of Science 3/1 (April 1, 2017): 38-41. https://izlik.org/JA84BF37WZ.
JAMA 1.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, Apr. 2017, pp. 38-41, https://izlik.org/JA84BF37WZ.
Vancouver 1.Mustafa Ali Dokuyucu, Ercan Çelik. The One Dimensional Keller-Segel Model. Eastern Anatolian Journal of Science [Internet]. 2017 Apr. 1;3(1):38-41. Available from: https://izlik.org/JA84BF37WZ