HE Ze-rong, WANG Mian-se, WANG Feng. Optimal Dynamical Balance Harvesting for a Class of Renewable Resources System[J]. Applied Mathematics and Mechanics, 2004, 25(4): 433-440.
Citation: HE Ze-rong, WANG Mian-se, WANG Feng. Optimal Dynamical Balance Harvesting for a Class of Renewable Resources System[J]. Applied Mathematics and Mechanics, 2004, 25(4): 433-440.

Optimal Dynamical Balance Harvesting for a Class of Renewable Resources System

  • Received Date: 2002-05-03
  • Rev Recd Date: 2003-09-09
  • Publish Date: 2004-04-15
  • 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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