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A Prey-Predator Fishery Model With A Relative Size Of Reserved Area
[Full Text]
AUTHOR(S)
Kulbhushan Agnihotri, Sheenu Nayyer
KEYWORDS
Relative size; Holling type II; Migration; Optimal harvesting; Pontryagin's Maximum Principle; MPAs.
ABSTRACT
A prey-predator fishery model having reserved and unreserved area, with prey dispersal in a two-patch environment, has been proposed and investigated in this work. The logistic growth is considered for the fish species in each area. Holling type-II predator functional response has been considered. Relative size of the reserve and unreserved area is responsible for increase as well as decrease the density of the fishes. The harvesting is applied on both prey in an unreserved area and on predator. The dynamics of the proposed system has been explored locally. The thresholds for existence of biological equilibrium points are obtained. Optimal harvesting policy has been examined by the Pontryagin's Maximum Principle. Finally, theoretical results acquired and verified with the assistance of numerical simulations through MATLAB.
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