Ferenc Hartung

University of Pannonia, Veszprém · Department of Mathematics

In this work, we investigate a uniform approximation of a nonautonomous delayed CNN-Hopfield-type impulsive system with an associated impulsive differential system where a partial discretization is introduced with the help of piecewise constant arguments. Sufficient conditions are formulated, which imply that the error estimate decays exponentially...

In this paper we consider a scalar linear delay equation with constant delay associated with an impulsive self-support condition. We define a numerical approximation scheme using a sequence of approximate delay equations with piecewise constant arguments, and we show its theoretical convergence. We present numerical examples to illustrate the appli...

In this paper we consider a class of nonlinear neutral functional differential equations with state-dependent delays. We study well-posedness and differentiability of the solution with respect to the parameters in a pointwise sense and also in the supremum norm.

In this paper we study ventilation patterns in a set of parameter dependent nonlinear delay equations with two transport delays modeling the human respiratory control system with peripheral and central control loops. We present a convergent numerical scheme suitable to perform simulations when all disturbances and system parameters are known, then...

In this paper we consider a class of delay differential equations of the form $\dot{x}(t)=\alpha (t) h(x(t-\tau), x(t-\sigma))-\beta(t)f(x(t))$, where $h$ is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and upper estimates of the limit inferior and the limit...

In this manuscript the system of nonlinear delay differential equations {equation presented} 1 ≤ i ≤ n is considered. Sufficient conditions are established for the uniform permanence of the positive solutions of the system. In several particular cases, explicit formulas are given for the estimates of the upper and lower limit of the solutions. In a...

This paper investigates the bounded input bounded output (BIBO) stability in a class of control system of nonlinear difference equations with several time delays. The proofs are based on our studies on the boundedness of the solutions of a general class of nonlinear Volterra difference equations with delays

In this paper we consider a class of functional differential equations with time-dependent delay. We show continuous differentiability of the solution with respect to the time delay function for each fixed time value assuming natural conditions on the delay function. As an application of the differentiability result, we give a numerical study to es...

In this paper we consider a class of differential equations with state-dependent delays. We show differentiability of the solution with respect to the initial function and the initial time for each fixed time value assuming that the state-dependent time lag function is piecewise monotone increasing. Based on these results, we prove a nonlinear vari...

Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering, and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-e...

In this paper we study parameter identification issues by computational means for a set of nonlinear delay equations which have been proposed to model the dynamics of a simplified version of the respiratory control system. We design specific inputs for our system to produce "information rich" output data needed to determine values of unknown parame...

In this paper we study parameter identification issues by computational means for a set of nonlinear delay equations which have been proposed to model the dynamics of a simplified version of the respiratory control system. We design specific inputs for our system to produce "information rich" output data needed to determine values of unknown parame...

This paper investigates the bounded input bounded output (BIBO) stability in a class of control system of nonlinear differential equations with time-delay. The proofs are based on our studies on the boundedness of the solutions of a general class of nonlinear Volterra integral equations.

In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the state-space, assuming that the state-dependent time lag function is piecewise strictly monotone.

In this paper we consider a class of differential equations with state-dependent delays. We show differentiability of the solution with respect to the initial function and the initial time for each fixed time value assuming that the state-dependent time lag function is strictly monotone increasing.

In this paper, we investigate the growth/decay rate of solutions of a class of nonlinear Volterra difference equations. Our results can be applied for the case when the characteristic equation of an associated linear difference equation has complex dominant eigenvalue with higher than one multiplicity. Illustrative examples are given for describing...

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.

In this paper we investigate the growth/decay rate of solutions of an abstract inte-gral equation which frequently arises in quasilinear differential equations applying a variation-of-constants formula. These results are applicable to some abstract equa-tions which appear in the theory of age dependent population models and also to some quasilinear...

In this paper we formulate a stability theorem by means of linearization around a trivial solution in the case of autonomous neutral functional differential equations with state-dependent delays. We prove that if the trivial solution of the linearized equation is exponentially stable, then the trivial solution of the nonlinear equation is exponenti...

In this paper we give a brief overview of the application of delay differential equations with piecewise constant arguments (EPCAs) for obtaining numerical approximation of delay differential equations, and we show that this method can be used for numerical approximation in a class of age-dependent population models. We also formulate an open probl...

In this paper we study exponential stability of the trivial solution of the state-dependent delay system ú x(t) = Pm i=1 Ai(t)x(ti(t, xt)). We show that under mild assumptions, the trivial solution of the state-dependent system is exponentially stable, if and only if the trivial solution of the corre- sponding linear time-dependent delay system ú y...

In this paper we study exponential stability of the trivial solution of the state-dependent delay system ẋ(t) = ∑i=1m A i(t)x(t - τi(t, xt)). We show that under mild assumptions, the trivial solution of the state-dependent system is exponentially stable if and only if the trivial solution of the corresponding linear time-dependent delay system ẏ(t)...

In this paper we give a sufficient condition to imply local and global asymptotic attractivity of the equilibrium of the Cohen-Grossberg neural network with time-dependent delays of the form

In this paper we consider a class of nonlinear neutral differential equations with state-dependent delays. We study well-posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite-dimensional parameters in a pointwise sense and also in the C- and W1,∞-norms.

In this paper we formulate sufficient conditions for the asymptotic stability of linear delay systems of the form x(k)(t) = - (l=0)Sigma(m) (j=1)Sigma(n) a(kj)((l))x(j)(t - tau((l))(kj)), k = 1,...,n, t >= 0, where a(kj)((0)), a(kj)((l)) epsilon R, tau((0))(kj) = 0, tau((l))(kj) >= 0, k j = 1,...,n,l = 1,...,m. In order to apply our results, we giv...

Unwanted relative vibrations between the tool and the workpiece represent significant challenges in high-speed machining. In order to avoid this problem, one needs to specify ranges for system parameters (spindle speed, depth of cut) for which the process is stable, i.e., to obtain a so-called stability chart. Such stability charts usually can only...

We introduce a parameter identification algorithm and establish its theoretical convergence on initial value problems governed by neutral functional differential equations with state-dependent delays. The discretization of the differential equation is based on an Euler-type approximation method using equations with piecewise constant arguments. Num...

In this paper, we study stability of periodic solutions of a class of nonlinear functional differential equations (FDEs) with state-dependent delays using the method of linearization. We show that a periodic solution of the nonlinear FDE is exponentially stable, if the zero solution of an associated linear periodic linear homogeneous FDE is exponen...

Traditional models of regenerative machine tool chatter use constant time delays assuming that the period between two sub-sequent cuts is a constant determined definitely by the spindle speed. These models result in delay-differential equations with constant time delay. If the vibrations of the tool relative to the workpiece are also included in th...

In this paper we study the asymptotic behavior and numerical approximation of the single neuron model equation ẋ(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...

In this paper we give a sufficient condition to imply global asymptotic stability of a delayed cellular neural network of the form $$ \dot x_i(t) = -d_i x_i(t)+ \sum_{j=1}^na_{ij} f(x_j(t)) +\sum_{j=1}^nb_{ij}f(x_j(t-\tau_{ij}))+u_i,\qquad t\geq0,\quad i=1,\ldots,n, $$ where $f(t)=\frac 12(|t+1|-|t-1|)$. In order to prove this stability result we n...

In this paper we study a parameter estimation method in func-tional differential equations with state-dependent delays using a quasilineariza-tion technique. We define the method, prove its convergence under certain conditions, and test its applicability in numerical examples. We estimate infi-nite dimensional parameters such as coefficient functio...

In this paper we prove that a constant steady-state of an autonomous state-dependent delay equation is exponentially stable if a zero solution of a corresponding linear autonomous equation is exponentially stable.

We consider a class of linear delay equations with perturbed time lags and present conditions which guarantee that the asymptotic stability of the trivial solution of the equation at hand is preserved under these perturbations. As an example we show how our results can be used to obtain an estimate on the maximum allowable sampling interval in the...

In this paper we prove theoretical convergence for a variety of parameter identification schemes, based on approximations by equations with piecewise constant arguments, for classes of neutral differential equations.

We consider a class of neutral functional differential equations with state-dependent delays, and discuss existence, uniqueness, and numerical approximation of solutions of corresponding initial value problems.

In this paper we study differentiability of solutions with respect to parameters in state-dependent delay equations. In particular, we give sufficient conditions for differentiability of solutions in theW1,pnorm (1⩽p

We establish limiting relations between solutions for a large class of functional differential equations with time- and state-dependent delays and solutions of appropriately selected sequences of approximating delay differential equations with piecewise constant arguments. The approximating equations, generated in the above process, lead naturally...

In this paper we study the numerical performance of a parameter identification technique, based on approximation by equations with piecewise constant arguments, on various classes of hereditary systems. The examples considered here include delay equations with state-dependent delays and neutral equations.

In this paper we establish an asymptotic formula for "small" solutions of the delay equation $\dot x(t) = a x(t-b|x(t)|)$, where $a$ and $b$ are positive constants.

Studies the effects of perturbations of time delays on the stability of a class of delay equations. The authors' goal is to obtain a “practical” condition, i.e., a norm bound on the perturbations corresponding to the particular system under consideration, which guarantees the preservation of stability under perturbations. It turns out that such con...

In this paper we study exponential stability of solutions of a class of nonlinear differ- ential equations including differential equations with state-dependent delays by means of linearization.

We consider a class of linear delay difference equations with perturbed time lags and present conditions which guarantee that the asymptotic stability of the trivial solution of the equation at hand is preserved under these perturbations. As an application of this perturbation result, we give sufficient conditions for asymptotic stability of scalar...

Kutatásaink a következő témakörökhöz kapcsolódtak: Megoldások aszimptotikus jellemzése és stabilitása; integrálegyenletek és egyenlőtlenségek mértékterekben; differenciálegyenletek megoldásainak paraméterektől való differenciálható függése, paraméterek becslése; állapotfüggő késleltetésű differenciálegyenletek stabilitása. A 2004-2007 kutatási idős...

Thesis (Ph. D.)--University of Texas at Dallas, 1995. Includes vita. Includes bibliographical references (leaves 169-172).