一类非线性延迟微分方程数值解的振动性分析

Oscillation Analysis of Numerical Solutions for a Kind of Nonlinear Delay Differential Equation

本文考虑一类非线性延迟微分方程-带有单峰造血率的造血模型数值解的振动性及非振动性。运用线性化理论,把非线性差分方程的振动性转化为其对应的线性差分方程的振动性,通过判断线性方程的特征方程根的情况,得到了非线性差分方程振动和存在非振动解的充分条件。对于非振动的数值解,证明了非振动的数值解最终都趋于方程的平衡解。为了更有力的说明我们的结果给出了相应的算例.

This paper is concerned with oscillation and non-oscillation of numerical solutions for nonlinear delay differential equation of hematopoiesis with a unimodal production rate. By linearization theory, oscillation of the nonlinear difference equation is transformed to that of the corresponding linear difference equation. By judging the roots of the characteristic equation of the linear difference equation, some conditions under which numerical solutions of the nonlinear difference equation are oscillatory and a non-oscillatory numerical solution exists are obtained. Moreover, the properties of non-oscillatory numerical solutions are investigated, that is, the non-oscillatory numerical solution tends to the equilibrium solution. To verify our results, we give numerical experiments.