Global Existence of Periodic Solutions in a Delayed Tumor-Immune Model

A. Kaddar; H. Talibi Alaoui

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 29-34
  • ISSN: 0973-5348

Abstract

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This paper is devoted to the study of global existence of periodic solutions of a delayed tumor-immune competition model. Also some numerical simulations are given to illustrate the theoretical results

How to cite

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Kaddar, A., and Talibi Alaoui, H.. Taik, A., ed. "Global Existence of Periodic Solutions in a Delayed Tumor-Immune Model." Mathematical Modelling of Natural Phenomena 5.7 (2010): 29-34. <http://eudml.org/doc/197662>.

@article{Kaddar2010,
abstract = {This paper is devoted to the study of global existence of periodic solutions of a delayed tumor-immune competition model. Also some numerical simulations are given to illustrate the theoretical results},
author = {Kaddar, A., Talibi Alaoui, H.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {tumor-immune model; delayed differential equations; Hopf bifurcation; periodic solutions},
language = {eng},
month = {8},
number = {7},
pages = {29-34},
publisher = {EDP Sciences},
title = {Global Existence of Periodic Solutions in a Delayed Tumor-Immune Model},
url = {http://eudml.org/doc/197662},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Kaddar, A.
AU - Talibi Alaoui, H.
AU - Taik, A.
TI - Global Existence of Periodic Solutions in a Delayed Tumor-Immune Model
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 29
EP - 34
AB - This paper is devoted to the study of global existence of periodic solutions of a delayed tumor-immune competition model. Also some numerical simulations are given to illustrate the theoretical results
LA - eng
KW - tumor-immune model; delayed differential equations; Hopf bifurcation; periodic solutions
UR - http://eudml.org/doc/197662
ER -

References

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  1. K.L. Cooke, Z. Grossman. Discrete delay, distributed delay and stability switches. Journal of Mathematical Analysis and Applications, 86 (1982), No. 2, 592–627. 
  2. M. Gałach. Dynamics of the tumor-immune system competition: the effect of time delay. Int. J. Appl. Comput. Sci., 13 (2003), No. 3, 395–406. 
  3. V.A. Kuznetsov, M.A. Taylor. Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis. Bull. Math. Biol., 56 (1994), No. 2, 295–321. 
  4. J. Wu. Symmetric functional differential equation and neural networks with memory. Trans. Am. Math. Sco., 350 (1998), No. 12, 4799–4838. 
  5. J. K. Hale, H. Koçak. Dynamics and bifurcations. Springer- Verlag, New York, 1991.  
  6. J. K. Hale, S.M. Verduyn Lunel. Introduction to functional differential equations. Springer- Verlag, New York, 1993.  

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