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Optimal Harvest Policy for Stably Bounded Logistic Equation

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Author:
No author available
Journal Title:
JOURNAL OF BIOMATHEMATICS
Issue:
1
DOI:
10.3969/j.issn.1001-9626.2004.01.003
Key Word:
Logistic方程;稳定有界函数;最终最优收获策略;欧拉方程;Logistic equation;Stably bounded function;Ultimately optimalharvest policy;Euler-Lagrange equation

Abstract: The exploitation of single population modelled by nonautonomousLogistic equation is considered in this paper. First we introduce a new concept ofstably bounded function which is a gerneralization of periodic function and almostperiodic function in the sense that they all have average value in R+. Then we de-fine a new harvest policy called ultimately optimal harvest policy which is useful todeal with our problem. We choose the average limiting maximum sustainable yieldper unit time as management objective, the corresponding optimal population level isdetermined. As an application, we give an example of Logistic equation with almostperiodic coefficients. It is shown that our results not only extend the classical resultsof Clark[1] for a population described by the autonomous Logistic equation but alsogeneralize results of Meng Fan and Ke Wang [2] for time-dependent Logistic equationwith periodic coefficients.

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