Dynamics of optimal harvesting in an Ammensal-Adversarial interaction

K. Shiva Reddy; Kottakkaran Sooppy Nisar; N. Phani Kumar; Choonkil Park; Ibrahim S. Yahia

Alexandria Engineering Journal (Dec 2022)

Dynamics of optimal harvesting in an Ammensal-Adversarial interaction

K. Shiva Reddy,
Kottakkaran Sooppy Nisar,
N. Phani Kumar,
Choonkil Park,
Ibrahim S. Yahia

Affiliations

K. Shiva Reddy: Department of Mathematics, Anurag University, Hyderabad, Telangana, India; Corresponding authors at: Department of Mathematics, Anurag University, Hyderabad, Telangana, India and Research Institute for Natural Sciences, Hanyang University, Seoul 04763, South Korea
Kottakkaran Sooppy Nisar: Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam bin Abdulaziz University, Saudi Arabia
N. Phani Kumar: Department of Mathematics, Vignan Institute of Technology and Science Hyderabad, India
Choonkil Park: Research Institute for Natural Sciences, Hanyang University, Seoul 04763, South Korea.; Corresponding authors at: Department of Mathematics, Anurag University, Hyderabad, Telangana, India and Research Institute for Natural Sciences, Hanyang University, Seoul 04763, South Korea
Ibrahim S. Yahia: Laboratory of Nano-Smart Materials for Science and Technology (LNSMST), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia; Research Center for Advanced Materials Science (RCAMS), King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia; Nanoscience Laboratory for Environmental and Biomedical Applications (NLEBA), Metallurgical Laboratory 1, Department of Physics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt

Journal volume & issue: Vol. 61, no. 12
pp. 12123 – 12128

Abstract

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This article discusses the stability of a two-species ecosystem composed of an ammensal (x) and an adversarial (y) species that are continuously harvested. A mathematical model is defined by a system of two nonlinear ordinary differential equations of first order. The considered system's boundedness is investigated. The local stability of the system is described using a variational matrix, while the global stability is examined using Lyapunov's function. The prerequisite for the system to exist in bionomic equilibrium has been identified. The ideal harvesting technique is determined using the maximal principle proposed by Pontryagin. In MATLAB simulations, the stability of the deterministic system is demonstrated for the specified set of parameters.

Published in Alexandria Engineering Journal

ISSN: 1110-0168 (Print); 2090-2670 (Online)
Publisher: Elsevier
Country of publisher: Egypt
LCC subjects: Technology: Engineering (General). Civil engineering (General)
Website: http://www.journals.elsevier.com/alexandria-engineering-journal/

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