Bifurcation analysis of a Leslie–Gower predator–prey system with fear effect and constant-type harvesting

This paper investigates the effect of fear effect and constant-type harvesting on the dynamic of a Leslie–Gower predator–prey model. Initially, an analysis is carried out to identify all potential equilibria and evaluate their stability. Furthermore, the dynamic behavior at these points is examined, revealing various bifurcations such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation. In particular, the model undergoes a degenerate Hopf bifurcation, which leads to the existence of two limit cycles. Additionally, we demonstrate that the Bogdanov–Takens bifurcation of codimension 2 occurs in this model. Ultimately, these findings are validated through numerical simulations, demonstrating that continuous harvesting or the significant fear effect is not conducive to either predator or prey surviving.