Prey-Predator Model with General Holling Type Response Function and Optimal Harvesting Policy

Dr. Dipankar Sadhukhan

doi:https://doi.org/10.14445/22315373/IJMTT-V53P521

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 3 | Year 2018 | Article Id. IJMTT-V53P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P521

Prey-Predator Model with General Holling Type Response Function and Optimal Harvesting Policy

Dr. Dipankar Sadhukhan

Citation :

Dr. Dipankar Sadhukhan, "Prey-Predator Model with General Holling Type Response Function and Optimal Harvesting Policy," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 3, pp. 172-179, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P521

Abstract

In this paper, we have considered a very general Holling type predator-prey system with selective harvesting and where both of the species follow logistic growth. The uniform boundedness of the system has been studied together with the conditions of existence. Also, we have obtained the criteria for local stability of various equilibrium points then considering suitable Lyapunov function, the global stability of the system has been discussed. After that using Pontryagin Maximal Principle, we have studied the optimal harvesting policy for the system. At the end, the problem has been illustrated through some numerical examples.

Keywords

Prey-predator system, Stability, Bionomic equilibrium, Optimal harvesting, Holling type response.

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