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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Dynamics of a Two Prey One Predator Fishery with Low Predator Density
verfasst von : T. Das, Rathindra Nath Mukherjee, K. S. Chaudhuri
Erschienen in: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
Verlag: Springer Berlin Heidelberg
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The present model is concerned with a multispecies fishery with two prey species both of which obeys the logistic law of growth and one predator species whose density is low. The predator consumes one of the prey species more intensively than the other because of its availability. For the predator species the growth function is taken as the model described by Smith. We assume that both the prey species are subjected to harvesting while the predator species is excluded from harvesting due to its low density. In this model we consider that the harvesting effort E is a function of time t. For optimization, we use the concept of generalized Legendre condition. The trajectory for the optimal singular extremal is derived and the optimal singular control is determined. Lastly, one numerical example is taken up and graph for steady state is drawn to illustrate the results.