We introduce a delay differential equation model which describes how fish are harvested

In this paper , by using fixed point theorem , upper and lower solution’s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper. Keywords—Banach space , boundary value problem , differential equation , delay .

In this paper the efficient implementation of numerical software for solving delay differential equations is addressed. Several strategies that have been developed over the past 25 years for improving the efficiency of delay differential equation solvers are described. Of particular interest is a new method of automatically constructing the network dependency graph used in tracking derivative d...

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 study scalar first order linear autonomous neutral delay differential equations with distributed type delays. This article presents some new results on the asymptotic behavior, the nonoscillation and the stability. These results are obtained via a real root (with an appropriate property) of the characteristic equation. Applications to the special cases such as (non-neutral) delay differentia...

We consider a certain second-order nonlinear delay differential equation and prove that the all solutions oscillate when proper impulse controls are imposed. An example is given. c © 2006 Elsevier Science Ltd. All rights reserved. Keywords—Delay differential equations, Second-order, Nonlinear, Oscillation, Impulses.