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On the delay differential equation y'(x) = ay(τ(x)) + by(x)

Jan Čermák (1999)

Annales Polonici Mathematici

The paper discusses the asymptotic properties of solutions of the scalar functional differential equation . Asymptotic formulas are given in terms of solutions of the appropriate scalar functional nondifferential equation.

On the dimension of the solution set to the homogeneous linear functional differential equation of the first order

Alexander Domoshnitsky, Robert Hakl, Bedřich Půža (2012)

Czechoslovak Mathematical Journal

Consider the homogeneous equation where is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.

On the dynamics of a vaccination model with multiple transmission ways

Shu Liao, Weiming Yang (2013)

International Journal of Applied Mathematics and Computer Science

In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number below unity....

On the Dynamics of an Impulsive Model of Hematopoiesis

C. Kou, M. Adimy, A. Ducrot (2009)

Mathematical Modelling of Natural Phenomena

We propose and analyze a nonlinear mathematical model of hematopoiesis, describing the dynamics of stem cell population subject to impulsive perturbations. This is a system of two age-structured partial differential equations with impulses. By integrating these equations over the age, we obtain a system of two nonlinear impulsive differential equations with several discrete delays. This system describes the evolution of the total hematopoietic stem cell populations with impulses. We first examine...

On the dynamics of equations with infinite delay

Dalibor Pražák (2006)

Open Mathematics

We consider a system of ordinary differential equations with infinite delay. We study large time dynamics in the phase space of functions with an exponentially decaying weight. The existence of an exponential attractor is proved under the abstract assumption that the right-hand side is Lipschitz continuous. The dimension of the attractor is explicitly estimated.

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