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.

Keywords:

• Oscillation
• nonlinear
• delay differential equations
• numerical methods
• population dynamics

AMS Sub ject Classification:

• 34M10