The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...

Neutral delay differential equations contain the derivative of the unknown function both with and without delays. Some new phenomena can appear, hence the theory of neutral delay differential equations is even more complicated than the theory of non-neutral delay equations. The oscillatory behavior of the solutions of neutral systems is of importance in both the theory and applications, such as...

The simplest chaotic delay differential equation with a sinusoidal nonlinearity is described, including the route to chaos, Lyapunov exponent spectrum, and chaotic diffusion. It is prototypical of many other high-dimensional chaotic systems. © 2007 Elsevier B.V. All rights reserved. PACS: 02.30.Ks; 02.30.Oz; 05.45.-a; 05.45.Jn; 05.45.Pq

l~(t) = r(t)N(t) a bkN(hk(t)) cz(t)N(gl(t)), t >_ O, l = l N(t )=~( t ) , t<O, N(O)=No, is considered. The existence and the bounds of positive solutions are studied. Sufficient conditions for the extinction of the solution are presented. © 2005 Elsevier Ltd. All rights reserved. K e y w o r d s D e l a y logistic equations, Linear harvesting, Positive solutions, Extinction of the population, S...

The purpose of this paper is to study oscillation and asymptotic behavior of solutions to a third order linear delay differential equation . All righ in part t Umeå Baculíko y000ðtÞ þ pðtÞy0ðtÞ þ qðtÞyðsðtÞÞ 1⁄4 0: New comparison theorems deduce oscillation of the given third order delay differential equation via application of known oscillation criteria to associated first order delay differen...

in this article differential transformation method (dtms) has been used to solve neutral functional-differential equations with proportional delays. the method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. exact solutions can also be obtained from the kno...

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...

The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a γ-Hölder continuous process with γ > 1/2 (e.g. a fractional Brownian motion with Hurst parameter greater than 1/2). It is shown that its solution depends continuously on the coefficients and the initial data. Two applications of this result are given: the convergence of solutions to ...

Nonlinear difference equations of higher order are important in applications; such equations appear naturally as discrete analogues of differential and delay differential equations which model various diverse phenomena in biology, ecology, economics, physics and engineering. The study of dynamical properties of such equations is of great importance in many areas. The autonomous difference equat...

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...