一类二阶系统的定量分析

Quantitative Analysis for a Class of Second Order Systems

对一类非线性二阶时滞系统求得一致有效渐近展开式,给出了共振解的近似解析公式,并推广了一些已知结果.

In this paper, the resonance problems of nonlinear time - delay systems are studied. The famous method of multiple scales is successfully extended to the time - delay systems. It provides us with great convenience to study the nonlinear systems with time lag. As to the complex forced oscillation problems of a class of nonlinear time - delay systems with damping and general force, this paper gets a uniformly valid asymptotic expansion according to the distinct circumstance of resonance and also gives an approximate analytic formula which is very simple and explicit. By using this formula, we can conveniently get approximate analytic solutions, especially amplitude, frequency, periodic and phase etc. from a great number of the resonance problems of time - delay oscillation systems. The research conclusions of paper and others are also included in our paper as simple corollaries. Key words： nonlinear system; resonance; analytic solution