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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Communicated by Lin Zong-chi, Original Member of Editorial Committee, AMM
Foundation item: the National Natural Science Foundation of China (19971066)
Biography: HE Ze-rong (1963 ∼), Associate Professor, Doctor
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Ze-rong, H., Mian-sen, W. & Feng, W. Optimal dynamical balance harvesting for a class of renewable resources system. Appl Math Mech 25, 475–482 (2004). https://doi.org/10.1007/BF02437532
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DOI: https://doi.org/10.1007/BF02437532