We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant difference equation such that its stability implies stability of the equation with a distributed delay and a finite memory. This result is, generally speaking, incor...

Introduction Time discretization approximation schemes for solutions of stochastic dierential equations have been studied by many people and are treated, e.g. in the book of Kloeden-Platen [Kl-Pl92]. Since heat kernels are the probability densities of the law of solutions, it might be worthwhile to ask if these approximation schemes provide a natural scheme of approximation for heat kenrnels. P...

In this paper, we proposed a numerical integration method for the solution of singularly perturbed delay differential equation with dual layer behaviour. In this method, an asymptotically equivalent first order neutral type delay differential equation is obtained from the second order singularly perturbed delay differential equation and employed Trapezoidal rule on it. Then, linear interpolatio...

With the development of modern society, research on properties of ordinary differential equation is becoming one of the hotspots in mathematical field. Neutral differential equation which is usually generated in natural science and engineering field is always extensively concerned by many scientific researchers for it can effectively describe multiple complex phenomena in natural world. In rece...

in this paper, a three dimensional mathematical model for htlv-1infection with intracellular delay and immune activation delay is investigated.by applying the frequency domain approach, we show that time delays candestabilize the ham/tsp equilibrium, leading to hopf bifurcations and sta-ble or unstable periodic oscillations. at the end, numerical simulations areillustrated.

Models with a time delay often occur, since there is a naturally occurring delay in the transmission of information. A model with a delay can be noninvertible, which in turn leads to qualitative differences between the dynamical properties of a delay equation and the familiar case of an ordinary differential equation. We give specific conditions for the existence of noninvertible solutions in d...

In this paper, some new types of delay integral inequalities on time scales are established, which can be used as a handy tool in the investigation of making estimates for bounds of solutions of delay dynamic equations on time scales. Our results generalize the main results in [15, 16, 17], and some of the results in [18, 19]. Key–Words: Delay integral inequality; Time scale; Integral equation;...

Nowadays, dispersive mirrors are able to cover the wavelength range of 4.5 optical octaves and can be used from 220 nm up to 4500 nm. Various design approaches to dispersive mirrors in visible and near IR are briefly discussed. We consider in more detail two dispersive mirrors representing extreme cases. The first one is a mirror working in the range of 290−360 nm and providing group delay dis...

We systematically study the pulse advance and pulse compression in light propagation through a transparent, anomalously dispersive medium. Using an Argand diagram, we show that pulse compression is the only form of pulse distortion, while other forms of pulse distortion can be eliminated. Experimentally, we implement a dual-band electronic amplifier to measure the negative pulse group delay and...

This paper presents an asymptotic state observer for the class of nonlinear dynamic systems with time-delay both in the dynamic equation and in the output equation. In previous works state observers have been studied only for nonlinear systems with delay in the state equation and without delay in the output equation and for nonlinear system with only output delay. Su±cient conditions are given ...