中文摘要：

讨论非线性时标动态系统的定性分析。首先讨论了2个基本性质，并提出了容许曲线的概念。根据步差函数μ（t），时标动态方程的右端函数z（t）可分为离散和连续2种情况，离散点时将在不同容许曲线上跳动，连续情况将沿着容许曲线前进。在此基础上，对平面时标动态Volterra竞争模型进行定性分析。用时标动态方程进行模拟自然界中的两种群竞争，当争夺环境资源时将在有限时间内其中一种群会突然死亡。

英文摘要：

Qualitative analysis of nonlinear dynamic system on time - scales is studied. Two properties are firstly discussed, and the concept ＂contain curve＂ is brought. Based on the graininess function μ（t） , function z（t） of dynamic system on time - scales can be divided into two cases; z（t） jumps from one contain curve to another in discrete points. While z（t） is along contain curve in continuous time t. The, n the planar Volterra competitive system on time- scales is qualitatively analyzed. Applying the conclusion to the competition between two populations, the death of one population in finite, time can be exphlined.