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Zbl 0940.92030
Fan, Meng; Wang, Ke
Optimal harvesting policy for single population with periodic coefficients. (English)
[J] Math. Biosci. 152, No.2, 165-177 (1998). ISSN 0025-5564

Summary: We examine the exploitation of a single population modeled by a time-dependent logistic equation with periodic coefficients. First, it is shown that the time-dependent periodic logistic equation has a unique positive periodic solution, which is globally asymptotically stable for positive solutions, and we obtain its explicit representation. Further, we choose the maximum annual-sustainable yield as the management objective, and investigate the optimal harvesting policies for constant harvest and periodic harvest. \par The optimal harvest effort that maximizes the annual-sustainable yield, the corresponding optimal population level, the corresponding harvesting time-spectrum, and the maximum annual-sustainable yield are determined, and their explicit expressions are obtained in terms of the intrinsic growth rate and the carrying capacity of the considered population. Our interesting and brief results generalize the classical results of {\it C. W. Clark} [Mathematical bioeconomics. The optimal management of renewable resources. (1976; Zbl 0364.90002)] for a population described by the autonomous logistic equation in renewable resources management.

MSC 2000:: *92D40 Ecology
49N20 Periodic optimization
49J15 Optimal control problems with ODE (existence)

Keywords: Euler-Lagrange equation; havesting time-spectrum; time-dependent logistic equation; periodic coefficients; optimal harvesting policies

Citations: Zbl 0364.90002

Cited in: Zbl 1129.49308 Zbl 1079.92061

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