Abstract

In this paper we propose a new model of harvesting fish population. This model is particularly applicable to those types of fish population which reproduce at a particular time of the year and this cycles continue throughout the life of the fish population. Many of the species including many types of fish follow such cyclic behaviour of reproduction. The model assumes the minimum and the maximum fraction of harvesting and guarantee the survival of the species and at the same time optimal harvesting. The model is analyzed both graphically and algebraically.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 30
Issue: 4
Year: 2017

DOI: 10.12732/ijam.v30i4.6

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References

1. [1] M. Kot, Elements of Mathematical Ecology, Cambridge University Press, New York, NY (2011).
2. [2] L.V. Idels, M. Wang, Harvesting fisheries management strategies with modified effort function, International Journal of Modelling, Identification and Control, 3 (2008), 83-87.
3. [3] W. Jing, W. Ke, Optimal control of harvesting for single population, Applied Mathematics and Computation, 156 (2004), 235-247.
4. [4] W. Jing, W. Ke, The optimal harvesting problems of a stage-structured population, Applied Mathematics and Computation, 148 (2004), 235-247.
5. [5] W. John, M. Pamela, T. Eric, The relationship of fish harvesting capacity to excess capacity and overcapacity, Marine Resource Economics, 19 (2005), 525-529.
6. [6] W. Li, K. Wang, Optimal harvesting policy for general stochastic logistic population model, Journal of Mathematical Analysis and Applications, 368 (2010), 420-428.
7. [7] D. Ludwig, A theory of sustainable harvesting, SIAM. J. Appl. Math., 55 (2001), 564-575.
8. [8] C.-H. Wang, S.-B. Wang, Theoretical development of Schaefer model and its application, In: 1st Meeting of the Scientific Committee of the Western and Central Pacific Fisheries Commission WCPFC-SC1. Institute of Oceanography, National Taiwan University, Taipei, Chinese-Taipei (2005).