The optimal harvesting problems of a stage-structured population. (English) Zbl 1037.92039

Summary: We consider a stage-structured population model with two life stages, immature and mature. The optimal harvesting policy for the considered population is given. We obtain the optimal harvesting effort, the maximum sustainable yield, the maximum sustainable economic rent and the corresponding population density.


92D40 Ecology
49N90 Applications of optimal control and differential games
34D05 Asymptotic properties of solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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[1] Clark, C. W., Mathematical Bioeconomics (1990), Wiley: Wiley New York · Zbl 0712.90018
[2] Huimin, L., The harvesting optimal problem of critical depensation systems, J. Biomech., 13, 6 (1998), (Chinese)
[3] Meng, F.; Ke, W., Study on harvesting population with diffusional migration, J. Syst. Sci. Comp., 14, 2 (2001) · Zbl 0976.92023
[4] Meng, F.; Ke, W., Optimal harvesting policy for single population with periodic coefficients, Math. Biosci., 152 (1998) · Zbl 0940.92030
[5] Wang, W.; Chen, L., A predator-prey system with stage structure for predator, Comput. Math. Appl., 33, 8 (1997)
[6] Zaghrout, A. A.S.; Attalah, S. H., Analysis of a model of stage-structured population dynamics growth with time state-dependent time delay, Appl. Math. Comput., 77 (1996) · Zbl 0848.92017
[7] Aiello, W. G.; Freedman, H. I.; Wu, J., Analysis of a model representing stage-structured population growth with state dependent time delay, SIAM, J. Appl. Math., 52, 3 (1992) · Zbl 0760.92018
[8] Murray, J. D., Mathematical Biology (1989), Springer-Verlag: Springer-Verlag Berlin Heidelberg, New York · Zbl 0682.92001
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