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Anca Veronica Ion

Publications and source records attributed to Anca Veronica Ion.

7 recordsLinked to original sources
arXiv2014

Study of the behaviour of proliferating cells in leukemia modelled by a system of delay differential equations

For the model of periodic chronic myelogenous leukemia considered by Pujo-Menjouet, Mackey et al., model consisting of two delay differential equations, the equation for the density of so-called "resting cells" was studied from numerical and qualitative point of view in several works. In this paper we focus on the equation for the density of proliferating cells and study it from a qualitative point of view.

math.DS↗
arXiv2014

"An example of Bautin-type bifurcation in a delay differential equation", plus errata

Some errors contained in the author's previous article "An example of Bautin-type bifurcation in a delay differential equation", JMAA, 329(2007), 777-789, are listed and corrected. Original abstract: In a previous paper we gave sufficient conditions for a system of delay differential equations to present Bautin-type bifurcation. In the present work we present an example of delay equation that satisfies these conditions.

math.DS↗
arXiv2013

On the computation of the third order terms of the series defining the center manifold for systems of delay differential equation

When studying a general system of delay differential equation with a single constant delay, we encounter a certain lack of uniqueness in determining the coefficient of one of the third order terms of the series defining the center manifold. We solve this problem by considering a perturbation of the considered problem, perturbation that allows us to remove the singularity. The result generalizes a similar result obtained for scalar differential equations (J. Dyn. Diff. Eqns., 24/2012).

math.DS↗
arXiv2012

Numerical investigation of the Bautin bifurcation in a delay differential equation modeling leukemia

In a previous work we investigated the existence of Hopf degenerate bifurcation points for a differential delay equation modeling leukemia and we actually found Hopf points of codimension two for the considered problem. If around the parameters corresponding to such a point we vary two parameters (the considered problem has five parameters), then a Bautin bifurcation should occur. In this work we chose a Hopf point of codimension two for the considered problem and perform numerical integration for parameters chosen in a neighborhood of the bifurcation point parameters. The results show that, indeed, we have a Bautin bifurcation in the chosen point.

math.DS↗
arXiv2012

Hopf points of codimension two in a delay differential equation modeling leukemia

This paper continues the work contained in two previous papers, devoted to the study of the dynamical system generated by a delay differential equation that models leukemia. Here our aim is to identify degenerate Hopf bifurcation points. By using an approximation of the center manifold, we compute the first Lyapunov coefficient for Hopf bifurcation points. We find by direct computation, in some zones of the parameter space (of biological significance), points where the first Lyapunov coefficient equals zero. For these we compute the second Lyapunov coefficient, that determines the type of the degenerate Hopf bifurcation.

math.DS↗
arXiv2010

New results concerning the stability of equilibria of a delay differential equation modeling leukemia

The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic solutions. Some stability results for the equilibria are also presented in these works, but they are incomplete and contain some errors. Our work aims to complete and to bring corrections to those results. Both Lyapunov first order approximation method and second Lyapunov method are used.

math.DS↗