Geodesic
The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response
Radouane Yafia1
1 Faculté Polydisciplinaire Université Ibn Zohr B.P. 638, Ouarzazate, Morocco
Applicationes Mathematicae, Tome 36 (2009) no. 3, pp. 349-364.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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).
DOI : 10.4064/am36-3-7
Keywords: consider system delay differential equations modelling tumor immune system competition negative immune response three positive stationary points dynamics first positive solutions studied terms local stability particularly interested study hopf bifurcation problem predict occurrence stability limit cycle bifurcating second positive stationary point delay taken parameter crosses critical values results obtained provide oscillations given numerical study given galach

Radouane Yafia 1

1 Faculté Polydisciplinaire Université Ibn Zohr B.P. 638, Ouarzazate, Morocco 
@article{10_4064_am36_3_7,
     author = {Radouane Yafia},
     title = {The effect of time delay and {Hopf} bifurcation
 in a tumor-immune system competition model
 with negative immune response},
     journal = {Applicationes Mathematicae},
     pages = {349--364},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {2009},
     doi = {10.4064/am36-3-7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am36-3-7/}
}
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
SP  - 349
EP  - 364
VL  - 36
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am36-3-7/
DO  - 10.4064/am36-3-7
LA  - en
ID  - 10_4064_am36_3_7
ER  - 
%0 Journal Article
%A Radouane Yafia
%T The effect of time delay and Hopf bifurcation
 in a tumor-immune system competition model
 with negative immune response
%J Applicationes Mathematicae
%D 2009
%P 349-364
%V 36
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/am36-3-7/
%R 10.4064/am36-3-7
%G en
%F 10_4064_am36_3_7
Radouane Yafia. The effect of time delay and Hopf bifurcation
 in a tumor-immune system competition model
 with negative immune response. Applicationes Mathematicae, Tome 36 (2009) no. 3, pp. 349-364. doi : 10.4064/am36-3-7. http://geodesic.mathdoc.fr/articles/10.4064/am36-3-7/

Cité par Sources :