István Gyori

Asymptotic integration of delay differential systems

On considere des equations non autonomes qui sont asymptotiquement autonomes et on cherche des formules pour les solutions aux grandes valeurs de la variable independante

Stability analysis of a single neuron model with delay

In this paper we study the asymptotic behavior and numerical approximation of the single neuron model equation x(t)=-dx(t)+af(x(t))+bf(x(t-τ))+I, t ≥ 0 (1), where d > 0 and f(x)=0.5(|x+ 1| - |x-1|). We obtain new sufficient conditions for global asymptotic stability of constant equilibriums of (1), give several numerical examples to illustrate our results, and formulate conjectures on the asymptotic behavior of the solutions based on our numerical experiments.

On admissibility of the resolvent of discrete Volterra equations

Suppose that a pair of sequence spaces is admissible with respect to a discrete linear Volterra operator. This paper gives sufficient conditions for the same pair of spaces to be admissible with respect to the associated resolvent operator. The spaces considered include spaces of weighted bounded and weighted convergent sequences. Classes of discrete kernels are discussed for which the appropriate weight sequences are not purely exponential, but the product of an exponential and a slowly decaying sequence.

Oscillations of retarded differential equations of the neutral and the mixed types

Abstract This paper is devoted to the study of the oscillation of solutions of delay differential equations of the neutral and mixed types. Some general results are proved for certain general Volterra type neutral differential equations and many particular cases are discussed.

Numerical approximation of neutral differential equations on infinite interval

In this paper we study numerical approximation of linear neutral differential equations on infinite interval using equations with piecewise constant arguments. As an application of our approximation results, we obtain stability theorems for some classes of linear delay and neutral difference equations.

Some mathematical aspects of modelling cell population dynamics

Abstract The purpose of this paper is to discuss different types of models of cell population dynamics based on differential equations and to point out the connection between them. From the starting point of the McKendrick/Von Foerster type model we derive Lotka-Volterra type integral equations, and some delaying-differential equations. We establish a connection between the original partial differential equation model and the Takahashi ordinary differential equations model, based on compartmental analysis, by means of a numerical procedure named “the method of lines”.