Turkish Journal of Computer and Mathematics Education
Journal license

Journal

Turkish Journal of Computer and Mathematics Education


Volume
& Issue

Volume 11, Issue 3


Published
on


Pages

1339-1350


DOI

Article

Optimal Harvesting of Three Species Dynamic Model with Bionomic Equilibrium


Authors

M. Gunasekarana Affiliation:
Assistant Professor, PG Department of Mathematics, Sri Subramaniya Swami Government Arts College, Tiruttani – 631 209, India
and A.m. Sarravanaprabhu* Affiliation:
Assistant Professor, Department of Mathematics, St. Thomas College of Arts and Science, Koyambedu, Chennai – 600 044, India and Research Scholar, PG Department of Mathematics, Sri Subramaniya Swami Government Arts College, Tiruttani – 631 209, India


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.


Keywords

Prey, Middle-level Predator, Top-level Predator, Equilibrium point, Stability Analysis, Optimal Harvesting, Quantitative Bionomic Equilibrium, Routh Hurwitz Criterion, Lyapunov Function


Citation

Gunasekarana, M. & Sarravanaprabhu, A. (2020). Optimal harvesting of three species dynamic model with bionomic equilibrium. Turkish Journal of Computer and Mathematics Education, 11(3), 1339–1350.

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