Theoretical and numerical bifurcation analysis in a prey–predator model with prey harvesting effort

This paper explores the influence of harvest efforts on a discrete-time prey-predator model. We established the stability criteria for fixed points in the proposed model. We investigate codim-1 and codim-2 bifurcations, exploring a range of multiple and generic bifurcations within the discrete model. The model demonstrates fold, flip, and Neimark-Sacker bifurcations, as well as resonances such as 1:2, 1:3, and 1:4 at distinct fixed points. Through the application of the critical normal form theorem and bifurcation theory, we calculate normal form coefficients for each bifurcation. Our results show that an excessive prey harvest rate can actually destabilize the model dynamics. Numerical simulations validate our findings, shedding light on the intricate dynamics of the system.