Displaying similar documents to “Dimensional reduction of nonlinear time delay systems.”

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...

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...

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...

Computation of double Hopf points for delay differential equations

Yingxiang Xu, Tingting Shi (2015)

Open Mathematics

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Relating to the crucial problem of branch switching, the calculation of codimension 2 bifurcation points is one of the major issues in numerical bifurcation analysis. In this paper, we focus on the double Hopf points for delay differential equations and analyze in detail the corresponding eigenspace, which enable us to obtain the finite dimensional defining system of equations of such points, instead of an infinite dimensional one that happens naturally for delay systems. We show that...

Hybrid matrix models and their population dynamic consequences

Sanyi Tang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation...