Holling-Tanner prey-predator model with Beddington-DeAngelis functional response including delay

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.

Automated summary

This paper presents a combined bioeconomic harvesting model that integrates the Holling-Tanner prey-predator competition model with Beddington-DeAngelis functional response and two different delays. The steady state points and their existence in the proposed model are discussed, along with the conditions for local stability and Hopf bifurcation. The study also employs center manifold theory to determine the stability and direction of bifurcating periodic solutions. Numerical simulations and graphical representations are provided to demonstrate the effects of various parameters. The paper concludes with a summary of findings and suggestions for future research.