Holling-Tanner prey-predator model with Beddington-DeAngelis functional response including delay. (2nd January 2022)

• Record Type: Journal Article
• Authors: Jana, Abhijit; Kumar Roy, Sankar
• Is Part Of: International journal of modelling & simulation. Volume 42:Number 1(2022)
• Page Start: 86
• Page End: 100
• Publication Date: 2022-01-02
• Subjects: Holling-Tanner model -- Beddington-DeAngelis functional response -- Hopf bifurcation -- center manifold theory -- bionomic equilibrium; Mathematical models -- Periodicals; Simulation methods -- Periodicals; Mathematical models; Simulation methods; Periodicals; 003.3
• DOI: 10.1080/02286203.2020.1839168
• Languages: English
• ISSNs: 0228-6203

Abstract

ABSTRACT: This paper is designed based on the combined bioeconomic harvesting of Holling-Tanner prey-predator competition model with Beddington-DeAngelis functional response with two different delays. The situation and existence of the steady state points for proposed model are discussed. The conditions for local stability of the interior steady state points together with the existence of Hopf bifurcation at the interior steady state point are addressed. The situations for stability and the direction of bifurcating periodic solutions are obtained by using center manifold theory. Also total revenue is calculated using bionomic equilibrium, and it is maximized by using Pontryagin's maximum principle. Some numerical simulations together with pictorial representations are placed in the paper for showing the effects of various parameters in the considered model. Conclusions with the future study are described at last.