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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