稳定有界的Logistic方程的最优捕获策略(英文)

Optimal Harvest Policy for Stably Bounded Logistic Equation

考虑单种群非自治的Logiscic方程的开采问题。在R^+中都存在均值的意义下,作为周期和概周期函数的推广,首先给出稳定有界函数的概念。然后定义一个新的最终最优收获策略用于处理我们的问题。选择单位时间的最大持久收益的极限均值作为管理目标,同时得到了最佳的种群水平。作为应用,我们以概周期系数的Logistic方程为例,表明我们的结果不仅推广了经典的Clark关于自治的Logjstic方程的收获问题,而且推广了范猛和王克的关于周期的Logistic方程的收获问题的结果。

The exploitation of single population modelled by nonautonomous Logistic equation is considered in this paper. First we introduce a new concept of stably bounded function which is a gerneralization of periodic function and almost periodic function in the sense that they all have average value in R+. Then we define a new harvest policy called ultimately optimal harvest policy which is useful to deal with our problem. We choose the average limiting maximum sustainable yield per unit time as management objective, the corresponding optimal population level is determined. As an application, we give an example of Logistic equation with almost periodic coefficients. It is shown that our results not only extend the classical results of Clark for a population described by the autonomous Logistic equation but also generalize results of Meng Fan and Ke Wang for time-dependent Logistic equation with periodic coefficients.