非驻定的奇摄动系统的周期解

PERIODIC SOLUTIONS OF NONAUTONOMOUS SINGULARLY PERTURBED SYSTEMS

对非驻定的奇摄动系统来说,当退化系统的周期解非孤立时,文献及仅对特殊的系统进行了研究。本文针对一般非线性系统,在渐近稳定的条件下,得到了完全系统的周期解的存在性、唯一性及收敛性。

For nonautonomous singularly perturbed systems only the special systems were investigated in the papers [2], [3] and [4], whena periodic solution of the degenerate system being non-isolated. In this paper, we obtain the existence, uniqueness and the convergence of a periodic solution of the full system for general nonlinear systems under asymptotically stable conditions.