The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response

Radouane Yafia

Applicationes Mathematicae (2009)

  • Volume: 36, Issue: 3, page 349-364
  • ISSN: 1233-7234

Abstract

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We consider a system of delay differential equations modelling the tumor-immune system competition with negative immune response and three positive stationary points. The dynamics of the first two positive solutions are studied in terms of the local stability. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence and stability of a limit cycle bifurcating from the second positive stationary point, when the delay (taken as a parameter) crosses some critical values. The results obtained provide the oscillations given by the numerical study given in Galach (2003).

How to cite

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Radouane Yafia. "The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response." Applicationes Mathematicae 36.3 (2009): 349-364. <http://eudml.org/doc/279934>.

@article{RadouaneYafia2009,
abstract = {We consider a system of delay differential equations modelling the tumor-immune system competition with negative immune response and three positive stationary points. The dynamics of the first two positive solutions are studied in terms of the local stability. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence and stability of a limit cycle bifurcating from the second positive stationary point, when the delay (taken as a parameter) crosses some critical values. The results obtained provide the oscillations given by the numerical study given in Galach (2003).},
author = {Radouane Yafia},
journal = {Applicationes Mathematicae},
language = {eng},
number = {3},
pages = {349-364},
title = {The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response},
url = {http://eudml.org/doc/279934},
volume = {36},
year = {2009},
}

TY - JOUR
AU - Radouane Yafia
TI - The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response
JO - Applicationes Mathematicae
PY - 2009
VL - 36
IS - 3
SP - 349
EP - 364
AB - We consider a system of delay differential equations modelling the tumor-immune system competition with negative immune response and three positive stationary points. The dynamics of the first two positive solutions are studied in terms of the local stability. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence and stability of a limit cycle bifurcating from the second positive stationary point, when the delay (taken as a parameter) crosses some critical values. The results obtained provide the oscillations given by the numerical study given in Galach (2003).
LA - eng
UR - http://eudml.org/doc/279934
ER -

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