## A subdivision approach to the construction of approximate solutions of boundary-value problems with deviating arguments

Computers and Mathematics with Applications / 35 / 11 / 121-135 / CMAPD

Computers and Mathematics with Applications / 35 / 11 / 121-135 / CMAPD

Published in Applied Mathematics-A Journal of Chinese Universities

The paper gives two estimates of the distance between adjacent zeros of solutions of the first-order delay differential equations x′(t)+p(t)x(t−τ)=0 in the case when p(t)≥0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgr...

Published in Applied Mathematics-A Journal of Chinese Universities

In this paper, some sufficient conditions for oscillation of a first order delay differential equation with oscillating coefficients of the form x′(t)+p(t)x(t−τ)=0 are established, which improve and generalize some of the known results in the literature.

Published in BIT Numerical Mathematics

We consider the solution of delay differential equations (DDEs) by using boundary value methods (BVMs). These methods require the solution of one or more nonsymmetric, large and sparse linear systems. The GMRES method with the Strang-type block-circulant preconditioner is proposed for solving these linear systems. We show that if a Pk1,k2-stable BV...

Published in Journal of Applied Mathematics and Computing

In this paper we investigate the qualitative behaviour of numerical approximation to a class delay differential equation. We consider the numerical solution of the delay differential equations undergoing a Hopf bifurcation. We prove the numerical approximation of delay differential equation had a Hopf bifurcation point if the true solution does.

Published in Journal of Dynamics and Differential Equations

A delay differential equation is presented which models how the behavior of traders influences the short time price movements of an asset. Sensitivity to price changes is measured by a parameter a. There is a single equilibrium solution, which is non-hyperbolic for all a>0. We prove that for a1 a 2-dimensional global center-unstable manifold connec...

Published in Journal of Dynamics and Differential Equations

We consider a delay equation whose delay is perturbed by a small periodic fluctuation. In particular, it is assumed that the delay equation exhibits a Hopf bifurcation when its delay is unperturbed. The periodically perturbed system exhibits more delicate bifurcations than a Hopf bifurcation. We show that these bifurcations are well explained by th...

Published in Journal of Mathematical Biology

We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control, and allows us to compare the baroreflex influence on heart r...

Published in Annali di Matematica Pura ed Applicata

We consider a one-parameter family of delay differential equations which has been proposed as a model for a prize and prove that at a critical parameter where the linearization at equilibrium has a double zero eigenvalue periodic solutions bifurcate off with periods descending from infinity.

Published in Bioprocess and Biosystems Engineering

The phasing technique is a method for synchronizing cell populations in a bioreactor. Periodic changes of substrate supply and depletion can provoke a cell cycle phasing of originally stochastic scattered proliferation patterns. Synchronized cell populations characterized by changes in DNA content distribution can be monitored by flow cytometry. Th...