×

Optimal harvesting policy for general stochastic logistic population model. (English) Zbl 1187.92081

Summary: We consider some optimal harvesting policies for a general stochastic logistic population model. For two management objectives, that are the maximum sustainable yield and the maximum retained profits, the optimal harvesting policies are obtained. Meanwhile, the optimal harvest effort, the maximum of expectation of sustainable yield (or retained profits) and the corresponding variance are given.

MSC:

92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
34F05 Ordinary differential equations and systems with randomness
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Clark, C. W., Mathematical Bioeconomics: The Optimal Management of Renewal Resources (1976), Wiley: Wiley New York · Zbl 0364.90002
[2] Clark, C. W., Mathematical Bioeconomics: The Optimal Management of Renewal Resources (1990), Wiley: Wiley New York · Zbl 0712.90018
[3] Fan, M.; Wang, K., Optimal harvesting policy for single population with periodic coefficients, Math. Biosci., 152, 165-177 (1998) · Zbl 0940.92030
[4] Zhang, X.; Shuai, Z.; Wang, K., Optimal impulsive harvesting policy for single population, Nonlinear Anal. Real World Appl., 4, 639-651 (2003) · Zbl 1011.92052
[5] Kar, T. K., Modelling and analysis of a harvested prey-predator system incorporating a prey refuge, J. Comput. Appl. Math., 185, 19-33 (2006) · Zbl 1071.92041
[6] Dong, L.; Chen, L.; Sun, L., Optimal harvesting policies for periodic Gompertz systems, Nonlinear Anal. Real World Appl., 8, 572-578 (2007) · Zbl 1152.34333
[7] Wang, J.; Wang, K., Optimal control of harvesting for single population, Appl. Math. Comput., 156, 235-247 (2004) · Zbl 1058.92052
[8] Gao, S.; Chen, L.; Sun, L., Optimal pulse fishing policy in stage-structured models with birth pulses, Chaos Solitons Fractals, 25, 1209-1219 (2005) · Zbl 1065.92056
[9] Beddington, J. R.; May, R. M., Harvesting natural populations in a randomly fluctuating environment, Science, 197, 463-465 (1977)
[10] Lande, R.; Engen, S.; Sæther, B. E., Optimal harvesting of fluctuating populations with a risk of extinction, Am. Nat., 145, 728-745 (1995)
[11] Alvarez, L. H.R.; Shepp, L. A., Optimal harvesting of stochastically fluctuating populations, Math. Biosci., 37, 155-177 (1998) · Zbl 0940.92029
[12] Alvarez, L. H.R., Optimal harvesting under stochastic fluctuations and critical depensation, Math. Biosci., 152, 63-85 (1998) · Zbl 0934.60073
[13] Shah, M. A.; Sharma, U., Optimal harvesting policies for a generalized Gordon-Schaefer model in randomly varying environment, Appl. Stoch. Models Bus. Ind., 19, 43-49 (2003) · Zbl 1035.60064
[14] Lu, H.; Wang, K., Autonomous single-species models and their optimal harvesting policies, J. Systems Sci. Math. Sci., 24, 2, 200-205 (2004) · Zbl 1060.92060
[15] Gardiner, C. W., Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (1985), Springer-Verlag: Springer-Verlag New York · Zbl 0862.60050
[16] Gard, T. C., Introduction to Stochastic Differential Equations (1988), Marcel Dekker: Marcel Dekker New York · Zbl 0682.92018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.