Asymptotic Analysis for a Class of Time Varying Harvested Logistic Model

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.