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Oscillation analysis of numerical solutions for nonlinear delay differential equations of population dynamics

    Jianfang Gao Affiliation
    ; Minghui Song Affiliation
    ; Mingzhu Liu Affiliation

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.

Keyword : Oscillation, nonlinear, delay differential equations, numerical methods, population dynamics

How to Cite
Gao, J., Song, M., & Liu, M. (2011). Oscillation analysis of numerical solutions for nonlinear delay differential equations of population dynamics. Mathematical Modelling and Analysis, 16(3), 365-375. https://doi.org/10.3846/13926292.2011.601768
Published in Issue
Aug 24, 2011
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