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

Radouane Yafia (2009)

Applicationes Mathematicae

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...

Two-mode bifurcation in solution of a perturbed nonlinear fourth order differential equation

Ahmed Abbas Mizeal, Mudhir A. Abdul Hussain (2012)

Archivum Mathematicum

In this paper, we are interested in the study of bifurcation solutions of nonlinear wave equation of elastic beams located on elastic foundations with small perturbation by using local method of Lyapunov-Schmidt.We showed that the bifurcation equation corresponding to the elastic beams equation is given by the nonlinear system of two equations. Also, we found the parameters equation of the Discriminant set of the specified problem as well as the bifurcation diagram.

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