一类Logistic时变收获模型的渐近分析

Asymptotic Analysis for a Class of Time Varying Harvested Logistic Model

研究一类含小参数的Logistic时变收获模型问题。采用匹配法构造其近似解,通过上下解法证明近似解的一致有效性,并给出近似解与精确解之间的误差估计。运用非线性多重尺度法,获得在更长时间范围内的形式渐近解。

A class of the time varying harvested Logistic model with small parameters was studied.The matching method was empoyed to construct the approximate solution of the model,and the uniform validity of the approximate solution was proved via methods of upper and lower solution.At the same time,the error estimate between the approximate solution and the exact solution was given.According to the nonlinear method of multiple scales,the formal asymptotic solution for longer periods of time was obtained.