Oscillation Analysis of Numerical Solutions for Nonlinear Delay Differential Equations of Population Dynamics

Abstract

This paper is concerned with oscillations of numerical solutions for the nonlinear delay differential equation of population dynamics. The equation proposed by Mackey and Glass for a ”dynamic disease” involves respiratory disorders and its solution resembles the envelope of lung ventilation for pathological breathing, called Cheyne-Stokes respiration. Some conditions under which the numerical solution is oscillatory are obtained. The properties of non-oscillatory numerical solutions are investigated. To verify our results, we give numerical experiments.

Oscillation analysis of θ‐methods for the Nicholson's blowflies model

“…Wang et al [13] studied numerical oscillation of alternately advanced and retarded equation with piecewise continuous argument, the conditions of oscillation for the Â-methods are obtained. However, to the best of our knowledge, until now, very few results dealing with the oscillation of the numerical solution for nonlinear DDEs have been reported except for Gao et al [14]. Different from [14], in this article, we will study the numerical oscillation for (1.1).…”

“…However, to the best of our knowledge, until now, very few results dealing with the oscillation of the numerical solution for nonlinear DDEs have been reported except for Gao et al [14]. Different from [14], in this article, we will study the numerical oscillation for (1.1). Specifically, we will consider some sufficient conditions under which the numerical solution is oscillatory.…”

Oscillations of Numerical Solutions for Nonlinear Delay Differential Equations in the Control of Erythropoiesis

“…More recently, Wang et al [9] studied numerical oscillations of alternately advanced and retarded linear EPCA, the conditions of oscillations for the -methods are obtained. To the best of our knowledge, until now less attention had been paid for the oscillations of the numerical solutions for nonlinear delay differential equations except for [10]. Differently from [10], in our paper, we will investigate another nonlinear delay differential equation in the control of erythropoiesis and obtain some new results.…”

“…To the best of our knowledge, until now less attention had been paid for the oscillations of the numerical solutions for nonlinear delay differential equations except for [10]. Differently from [10], in our paper, we will investigate another nonlinear delay differential equation in the control of erythropoiesis and obtain some new results.…”

Numerical Oscillation Analysis for Gompertz Equation with One Delay

“…This research has been applied to many fields including biology, physics, ecology and so on. Nonetheless there are few papers have been published on the oscillation of numerical solutions of DDEs (see [3]- [6]). So we will consider numerical oscillation for Gompertz equation with one delay in this paper.…”