Fowler, A.C. McGuinness, M.J.
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...

Choi, Younsun
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...

Brunovský, Pavol Erdélyi, Alexander Walther, Hans-Otto
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...

Zhang, Chunrui Liu, Mingzhu Zheng, Baodong
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.

Lin, F. R. Jin, X. Q. Lei, S. L.
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...

Xianhua, Tang
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.

Xianhua, Tang Jianshe, Yu
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...

Qu, R. Agarwal, R.P.

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