一类带小时滞的非线性快慢系统的渐近解

研究了一类带小时滞的非线性快慢系统的初始值问题,在一定假设条件下,利用奇异摄动理论和校正函数法构造了该问题的形式渐近解,并利用微分不等式理论证明了渐近解的一致有效性.最后进行了算例分析,结果显示时滞能对快慢系统产生重要影响,并表明所述摄动方法是一个行之有效的近似解析方法.从而,可以利用得到的渐近解对系统的动力学行为进行更深层次地分析与研究.

Asymptotic solution for a class of nonlinear slow-fast system with small time delay

In this paper, the initial value problem for a class of nonlinear slow-fast systems with small time delay is considered. Under suitable assumptions and by using singular perturbation theory and the correction function method, the formal asymptotic solution of the problem is constructed. Then, by means of the differential inequalities theory, the uniformly validity of the asymptotic solution is proved. Finally, a numerical example is done, whose results reveal that time delay may have a significant impact on the slow-fast system, and show that the perturbation method is an effective approximate analytical method. Consequently, the behavior of the dynamic system can be better analyzed and studied by using the asymptotic solution.