Optimal Harvesting of Three Species Dynamic Model with Bionomic Equilibrium

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Dr.M.Gunasekaran, A.M.Sarravanaprabhu

Abstract

This paper presents three species, ecological models with optimal harvesting effect. The proposed model of species,
termed as Prey (P), Middle-level Predator (Q) and Top-level Predator (R) is formed by a set of first order non-linear differential
equation. This system initially examines all the possible equilibrium points for this planned model, subsequently investigates the
stability analysis, optimal harvesting and quantitative bionomic equilibrium aspect of the prey-predator species and their
continued existence in the ecological system. Finally, local and global stability were studied by using Routh Hurwitz criteria and
Lyapunov function respectively under positive equilibrium state

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