Bifurcation analysis and turing instability of the ecological model having Beddington–Deangelis-type functional response

In this study, a prey-predator model with a Beddington-DeAngelis-type functional response is considered. The qualitative analysis of the model, including local and global stability, as well as Hopf bifurcation, is analyzed. The permanence analysis of the model is also established. The diffusion-driven instability for the diffusive model is also analyzed. The numerical stability of the model is also derived by using the Routh-Hurwitz criteria. The numerical solution of the model is gained by using the Implicit finite difference scheme. Simulations are conducted for various parameter choices, and their applications in real life are explained.