Displaying similar documents to “Hopf bifurcation of a mathematical model for growth of tumors with an action of inhibitor and two time delays.”

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

Radouane Yafia (2009)

Applicationes Mathematicae

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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...

Time delays in proliferation and apoptosis for solid avascular tumour

Urszula Foryś, Mikhail Kolev (2003)

Banach Center Publications

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The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties...

Local Bifurcations in a Nonlinear Model of a Bioreactor

Dimitrova, Neli (2009)

Serdica Journal of Computing

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This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02– 359/2008. We consider a nonlinear model of a continuously stirred bioreactor and study the stability of the equilibrium points with respect to practically important model parameters. We determine regions in the parameter space where the steady states undergo transcritical and Hopf bifurcations. In the latter case, the stability of the emerged limit cycles is also studied. Numerical simulations...

Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers

Lan Zhang, Cheng Jian Zhang (2008)

Kybernetika

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A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider...