延迟微分方程的振动性广泛应用于物理学、疾病动力学、气象科学等众多领域。近年来，有关延迟微分方程数值振动性的研究主要针对于几类常系数的线性微分方程和少数非线性模型。本项目以混合型自变量分段连续的脉冲微分方程、多维中立型微分系统及非自治的Logistic模型为研究对象，研究这几类方程数值解的振动性以及数值方法对原方程振动行为的保持性。对于混合型自变量分段连续的脉冲微分方程，研究解析解的振动性，讨论用Runge-Kutta方法得到的数值解振动的条件以及数值方法保持解析解振动的条件，进一步探讨数值解插值函数零点与解析解零点之间的逼近关系；对于多维中立型微分系统、非自治的Logistic模型，讨论数值解振动的条件和theta-方法保持原系统振动的条件，同时讨论非振动数值解的渐近行为。本项目的研究不仅可以丰富延迟微分方程数值振动性分析的内涵，而且也为相关实际问题的解决提供新的方法和理论依据。

Oscillation of delay differential equations have been widely used in physics, disease dynamics, meteorology and many other fields. In recent years, the study about the oscillation of numerical solutions mainly focuses on several kinds of linear equations and a few of nonlinear modelings with constant coefficients. In this project, we regard mixed impulsive differential equations with piecewise continuous arguments, a multi-dimensional neutral differential system and a non-autonomous Logistic modeling as research subjects. Oscillation of numerical solutions for the three kinds of equations and preservation of oscillation for analytical solutions will be thoroughly analyzed and discussed. For the mixed impulsive differential equation with piecewise continuous arguments, oscillation of analytical solutions will be investigated. Also oscillation conditions of the numerical solution obtained by Runge-Kutta method and conditions of the numerical method preserving the oscillation of the analytical solution are mainly discussed. Zeros of the interpolation function for numerical solutions are investigated. Moreover, the relationship of zeros between the analytical solution and the interpolation function is studied. For a multi-dimensional neutral differential system and a non-autonomous Logistic modeling, conditions of the oscillation for numerical solutions will be obtained. Also the conditions under which theta-methods can preserve oscillation will be given. In the meantime, the asymptotic behavior of non-oscillatory numerical solutions will be discussed. The research of this project not only enrich the connotation of the numerical oscillation analysis for delay differential equations, but also provide new methods and theoretical basis for solving related practical problems.