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Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (4): 475-482.

• 论文 • 上一篇    

OPTIMAL DYNAMICAL BALANCE HARVESTING FOR A CLASS OF RENEWABLE RESOURCES SYSTEM

何泽荣1,2, 王绵森1, 王峰1   

  1. 1. Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, P. R. China;
    2. Faculty of Science, Hangzhou Institute of Electronic Engineering, Hangzhou 310037, P. R. China
  • 收稿日期:2002-05-03 修回日期:2003-09-09 出版日期:2004-04-18 发布日期:2004-04-18
  • 基金资助:
    the National Natural Science Foundation of China(19971066)

OPTIMAL DYNAMICAL BALANCE HARVESTING FOR A CLASS OF RENEWABLE RESOURCES SYSTEM

HE Ze-rong1,2, WANG Mian-sen1, WANG Feng1   

  1. 1. Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, P. R. China;
    2. Faculty of Science, Hangzhou Institute of Electronic Engineering, Hangzhou 310037, P. R. China
  • Received:2002-05-03 Revised:2003-09-09 Online:2004-04-18 Published:2004-04-18
  • Supported by:
    the National Natural Science Foundation of China(19971066)

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摘要： An optimal utilization problem for a class of renewable resources system is investigated. Firstly, a control problem was proposed by introducing a new utility function which depends on the harvesting effort and the stock of resources.Secondly, the existence of optimal solution for the problem was discussed. Then, using a maximum principle for infinite horizon problem, a nonlinear four-dimensional differential equations system was attained. After a detailed analysis of the unique positive equilibrium solution, the existence of limit cycles for the system is demonstrated. Next a reduced system on the central manifold is carefully derived, which assures the stability of limit cycles. Finally significance of the results in bioeconomics is explained.

Abstract: An optimal utilization problem for a class of renewable resources system is investigated. Firstly, a control problem was proposed by introducing a new utility function which depends on the harvesting effort and the stock of resources.Secondly, the existence of optimal solution for the problem was discussed. Then, using a maximum principle for infinite horizon problem, a nonlinear four-dimensional differential equations system was attained. After a detailed analysis of the unique positive equilibrium solution, the existence of limit cycles for the system is demonstrated. Next a reduced system on the central manifold is carefully derived, which assures the stability of limit cycles. Finally significance of the results in bioeconomics is explained.

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