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Year 2016, Volume: 4 Issue: 3, 204 - 211, 30.09.2016

Mustafa Ali Dokuyucu Ercan Celik

Abstract

References

  • 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).

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

Year 2016, Volume: 4 Issue: 3, 204 - 211, 30.09.2016

Mustafa Ali Dokuyucu Ercan Celik

Abstract



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.




Keywords

Chemotaxis Keller-Segel model

References

  • 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).
There are 9 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Mustafa Ali Dokuyucu

Ercan Celik This is me

Publication Date September 30, 2016
Published in Issue Year 2016 Volume: 4 Issue: 3

Cite

APA Dokuyucu, M. A., & Celik, E. (2016). Nonlinear diffusion for chemotaxis and birth-death process for Keller-Segel model. New Trends in Mathematical Sciences, 4(3), 204-211.
AMA Dokuyucu MA, Celik E. Nonlinear diffusion for chemotaxis and birth-death process for Keller-Segel model. New Trends in Mathematical Sciences. September 2016;4(3):204-211.
Chicago Dokuyucu, Mustafa Ali, and Ercan Celik. “Nonlinear Diffusion for Chemotaxis and Birth-Death Process for Keller-Segel Model”. New Trends in Mathematical Sciences 4, no. 3 (September 2016): 204-11.
EndNote Dokuyucu MA, Celik E (September 1, 2016) Nonlinear diffusion for chemotaxis and birth-death process for Keller-Segel model. New Trends in Mathematical Sciences 4 3 204–211.
IEEE M. A. Dokuyucu and E. Celik, “Nonlinear diffusion for chemotaxis and birth-death process for Keller-Segel model”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 204–211, 2016.
ISNAD Dokuyucu, Mustafa Ali - Celik, Ercan. “Nonlinear Diffusion for Chemotaxis and Birth-Death Process for Keller-Segel Model”. New Trends in Mathematical Sciences 4/3 (September 2016), 204-211.
JAMA Dokuyucu MA, Celik E. Nonlinear diffusion for chemotaxis and birth-death process for Keller-Segel model. New Trends in Mathematical Sciences. 2016;4:204–211.
MLA Dokuyucu, Mustafa Ali and Ercan Celik. “Nonlinear Diffusion for Chemotaxis and Birth-Death Process for Keller-Segel Model”. New Trends in Mathematical Sciences, vol. 4, no. 3, 2016, pp. 204-11.
Vancouver Dokuyucu MA, Celik E. Nonlinear diffusion for chemotaxis and birth-death process for Keller-Segel model. New Trends in Mathematical Sciences. 2016;4(3):204-11.
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