Optimal Dynamical Balance Harvesting for a Class of Renewable Resources System

HE Ze-rong; WANG Mian-se; WANG Feng

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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.

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.

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Optimal Dynamical Balance Harvesting for a Class of Renewable Resources System

1.
Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, P. R. China;

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

Abstract

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.
- renewable resource,
- optimal harvesting,
- stability,
- bifurcation,
- limit cycle

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References(12)

References

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