a survey on oscillation of impulsive delay differential equations this paper presents a systematic development of the oscillatory results for the linear and nonlinear impulsive delay differential equations we also discuss linearized oscillation theory and give some applications to mathematical biology

uniform asymptotic stability of impulsive differential difference equations of neutral type by lyapunov s direct method abstract an initial value problem for an impulsive system of differential difference equations of neutral type is considered the impulses take place at fixed moments by means of lyapunov s direct method sufficient conditions for uniform asymptotic stability of the zero solution of such systems are found

stability with respect to part of the variables in systems with impulse effect abstract effective sufficient conditions are found for stability with respect to part of the variables in systems of ordinary differential equations with impulse effect the approach presented is based on the specially introduced piecewise continuous ljapunov functions

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

high order runge kutta methods for impulsive delay differential equations abstract the purpose of this paper is to obtain high order runge kutta methods for nonlinear impulsive delay differential equations iddes in order to achieve the purpose continuity and smoothness of the exact solutions of iddes are analyzed and then the discontinuous points and non smooth points are chosen as a part of the nodes of the runge kutta methods furthermore it is proved that the pth order runge kutta method for iddes is also convergent of order p and some simple numerical examples are given to demonstrate the theoretical results

an existence result for first order impulsive functional differential equations in banach spaces abstract in this paper the leray schauder nonlinear alternative is used to investigate the existence of solutions to first order impulsive initial value problems for functional differential equations in banach spaces

linear multistep methods for impulsive delay differential equations abstract this paper deals with the convergence and stability of linear multistep methods for a class of linear impulsive delay differential equations numerical experiments show that the simpson s rule and two step bdf method are of order p 0 when applied to impulsive delay differential equations an improved linear multistep numerical process is proposed convergence and stability conditions of the numerical solutions are given in the paper numerical experiments are given in the end to illustrate the conclusion

stability of runge kutta methods in the numerical solution of linear impulsive differential equations this paper deals with the stability analysis of the analytic and numerical solutions of linear impulsive differential equations the numerical method with variable stepsize is defined the conditions that the numerical solutions preserve the stability property of the analytic ones are obtained and some numerical experiments are given

periodic first order linear neutral delay differential equations some new asymptotic and stability results are given for a first order linear neutral delay differential equation with periodic coefficients and constant delays the asymptotic behavior of the solutions and the stability of the trivial solution are described by the use of an appropriate real root of an equation which is in a sense the corresponding characteristic equation

asymptotic stability of impulsive control neutral type systems in this paper we consider a delay control system of neutral type applying lyapunov functions and razumikhin technique combining with an impulsive feedback control we established some criteria for asymptotic stability of the system an example is also discussed to illustrate the main results we show that by means of appropriate impulsive perturbations we can control the stability behaviour of the system

stability under persistent disturbances of impulsive differential difference equations of neutral type abstract effective sufficient conditions for stability under persistent disturbances of the zero solution of impulsive systems of differential difference equations of neutral type are found the main results are stated in a theorem in its proof an analogue of gronwall bellman s inequality for piecewise continuous functions is used as a corollary the existence of a global solution of a system with quadratic nonlinearities is proved for sufficiently small initial data

asymptotic and numerical stability of systems of neutral differential equations with many delays we are concerned with the asymptotic stability of a system of linear neutral differential equations with many delays in the form y t ly t email protected i 1dm iy email protected i email protected i 1dn iy email protected i where l m i n email protected c n x n i 1 2 d are constant complex matrices t i 0 i 1 2 d are constant delays and y t y 1 t y 2 t y n t t is an unknown vector valued function for t 0 we first establish a new result for the distribution of the roots of its characteristic function next we obtain a sufficient condition for its asymptotic stability and then we investigate the corresponding numerical stability of linear multistep methods applied to such systems one numerical example is given to testify our numerical analysis

a game theoretic approach to the optimal control of uncertain systems the issue of performance robustness is considered in a dynamic games framework where the goal is to find a feedback controller that stabilizes the system under all plant perturbations and that minimizes the value of a quadratic performance index under the worst perturbations to find a solution to this hard constrained problem an auxiliary soft constrained dynamic game problem is formulated it is shown that the solution to the auxiliary problem provides the solution to the original problem under the assumption that the solution to the original problem occurs on the boundary of the perturbations set the approach however can still be applied with modifications to the case when this assumption fails

the euler scheme and its convergence for impulsive delay differential equations this paper presents a fixed stepsize euler scheme for linear impulsive delay differential equations and considers its convergence we propose a method to take the partition nodes for the euler scheme employing the induction and the technique of inequality we obtain the order of convergence for euler scheme an example is given to illustrate the efficiency of our result

stability of linear impulsive neutral delay differential equations with constant coefficients abstract in this article we have developed a new method regarding asymptotic behavior and stability for the solutions of first order linear impulsive neutral delay differential equations with constant coefficients and constant delays the asymptotic behavior of the solutions and the stability of the zero solution were investigated using a real root suitable for the characteristic equation furthermore we obtained similar results for impulsive delay differential equations finally three examples are given for the stability of the zero solution of the impulsive neutral delay differential equation

against the convergence of the minor component analysis neurons we investigate the dynamical behavior of some linear neurons devised for the minor component analysis contrary to their convergence theorems our analysis reveals the existence of a divergence in a finite time

explicit conditions of exponential stability for a linear impulsive delay differential equation for a scalar delay differential equationx t k 1mak t x hk t 0 t 0 x t r hk t t with impulsive conditionsx j bjx j 0 limj j explicit exponential stability results are obtained

exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations this paper is concerned with exponential stability of a class of linear impulsive delay differential equations iddes exponential stability of this kind of equations is studied by the properties of delay differential equations ddes without impulsive perturbations when different delay differential equations ddes without impulsive perturbations are chosen different sufficient conditions for exponential stability of the linear impulsive delay differential equations iddes are provided numerical methods for this kind of equations are constructed the convergence and exponential stability of the numerical solutions are studied and some experiments are given

existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay abstract in this paper we discuss local and global existence and uniqueness results for first order impulsive functional differential equations with multiple delay we shall rely on a nonlinear alternative of leray schauder for the global existence and uniqueness we apply a recent nonlinear alternative of leray schauder type in frechet spaces due to m frigon and a granas resultats de type leray schauder pour des contractions sur des espaces de frechet ann sci math quebec 22 2 1998 161 168 the goal of this paper is to extend the problems considered by a ouahab local and global existence and uniqueness results for impulsive differential equations with multiple delay j math anal appl 323 2006 456 472