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).
@article{bwmeta1.element.bwnjournal-article-doi-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},
volume = {36},
year = {2009},
pages = {349-364},
zbl = {1180.34096},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-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) pp. 349-364. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-3-7/