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An Optimal Harvesting Policy for the Two Prey Species in a Three Species Ecological Model

T. Vidyanath, Narayan K. Lakshmi , Shahnaz Bathul

Abstract



In this study, a system of non-linear ordinary differential equations emerging from a three species ecological model with one predator feeding on two prey species is considered for stability analysis and optimal harvesting. Here we harvested both the prey species based on catch-per-unit-effort hypothesis and all the three species grows logistically. The positive equilibrium point of the proposed system has been identified and its local stability is analyzed using Routh-Hurwitz criteria. A suitable Lyapunov function is constructed and the global stability of the system is studied. The conditions for the occurrence of local and global stability are also provided. Also the bioeconomic equilibrium has been derived and by virtue of Pontryagin’s maximum principle, the optimal harvesting policy and its effects are discussed. Numerical simulation provides justification to the theoretical results.

Keywords


Prey-Predation; Global Stability; Bioeconomic equilibrium; Pontryagin’s maximum principle; Optimal harvesting.

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