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

• Main Authors: Jianfang Gao, Minghui Song, Mingzhu Liu
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2011-08-01
• Series: Mathematical Modelling and Analysis
• Subjects: Oscillation; nonlinear; delay differential equations; numerical methods; population dynamics
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/5539

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.