一类非线性奇异摄动自治微分系统的渐近解

Abstract

A class of generalized Lienard singular perturbation systems were considered. Firstly, the reduced solution to the system was obtained. Next, the outer solution was constructed by means of the singular perturbation method. Then, a stretch variable was introduced and the initial layer corrective term was found. Finally, the arbitrary-order asymptotic analytic expansion of the system solution was given and the uniform validity of the solution was proved. The proposed method with the basic theory has wide application values.