种群动力系统的数值解的振动性分析

OSCILLATION ANALYSIS OF NUMERICAL SOLUTIONS FOR NONLINEAR DELAY DIFFERENTIAL EQUATIONS OF POPULATION DYNAMICS

本文主要研究下面动力系统的非线性延迟微分方程x′(t)+αV_mx(t)x^p*(t-τ)/(β~p+x^p(t-τ))=λ,t≥0数值解的振动性.这是由Mackey和Glass提出来的关于动力系统疾病的方程.本文得到了数值方法振动的条件.同时对非振动的数值解的性质也做了研究,为了验证得到的结果,给出了数值算例.

This paper is concerned with oscillations of numerical solutions for the nonlinear delay differential equation of population dynamics x＇（t）＋αVmx（t）x^p（t-τ）/β^p＋x^p（t-τ）=λ,t≥0 The equation proposed by Mackey and Glass for a ＂dynamic disease＂. Some conditions under which the numerical method is oscillatory are obtained. The properties of non-oscillatory numerical solutions are investigated. To verify our results, we give numerical experiments.