Stability and Bifurcation Analysis of a Predator-Prey Model with Michaelis-Menten Type Prey Harvesting

Abstract

In this paper, we investigated stability and bifurcation behaviors of a preda-tor-prey model with Michaelis-Menten type prey harvesting. Sufficient con-ditions for local and global asymptotically stability of the interior equilibrium point were established. Some critical threshold conditions for transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation were explored analytically. Furthermore, It should be stressed that the fear factor could not only reduce the predator density, but also affect the prey growth rate. Finally, these theoretical results revealed that nonlinear Michaelis-Menten type prey harvesting has played an important role in the dynamic relationship, which also in turn proved the validity of theoretical derivation.