We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two...

We consider a nonhomogeneous linear delay difference equation with continuous variable and establish an asymptotic result for the solutions. Our result is obtained by the use of a positive root with an appropriate property of the so-called characteristic equation of the corresponding homogeneous linear (autonomous) delay difference equation. More precisely, we show that, for any solution, the l...

We formulate and study a one-dimensional single-species di¬usive-delay population model. The time delay is the time taken from birth to maturity. Without di¬usion, the delay di¬erential model extends the well-known logistic di¬erential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes. This delayed model is known to have simple globa...

We study the gravitational time delay in ray propagation due to rotating masses in the linear approximation of general relativity. Simple expressions are given for the gravitomagnetic time delay that occurs when rays of radiation cross a slowly rotating shell, equation (14), and propagate in the field of a distant rotating source, equation (16). Moreover, we calculate the local gravitational ti...

In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof th...

It is demonstrated that the method of steps for linear delay-differential equation together with the inverse Laplace transform can be used to find a converging sequence of polynomial approximants to the transcendental function determining stability of the delay equation. Numerical stability charts are shown to illustrate convergence. This approach can serve as a basis for an efficient numerical...

A kind of fourth-order delay differential equation is considered. Firstly, the linear stability is investigated by analyzing the associated characteristic equation. It is found that there are stability switches for time delay and Hopf bifurcations when time delay cross through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form me...

Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation ...

We are concerned with the exponential mean-square stability of two-step Maruyama methods for stochastic differential equations with time delay. We propose a family of schemes and prove that it can maintain the exponential mean-square stability of the linear stochastic delay differential equation for every step size of integral fraction of the delay in the equation. Numerical results for linear ...