摘要
We first prove some basic results on the periodic time scales, then on a special but practical periodic time scales T = ∪[k（α ＋ b）, k（α ＋ b） ＋ α], the asymptotic behavior of x^△= px is explored with specific emphasis given to how the graininess of the time scales affects stability. At last, we analyze the asymptotic properties of the solutions of planar linear dynamic system, and obtain some sufficient conditions for the stability of the equalibium （0, 0）.
We first prove some basic results on the periodic time scales, then on a special but practical periodic time scales T = ∪[k（α ＋ b）, k（α ＋ b） ＋ α], the asymptotic behavior of x^△= px is explored with specific emphasis given to how the graininess of the time scales affects stability. At last, we analyze the asymptotic properties of the solutions of planar linear dynamic system, and obtain some sufficient conditions for the stability of the equalibium （0, 0）.
基金
Project supported by the National Education Committee Doctoral Foundation of China (No.20020558092)the National Natural Science Foundation of China (No.10371135).
