Stability and bifurcation analysis of the predator-prey model with Michaelis-Menten type harvesting and immigration

This paper is interested in studying the asymptotic stability and bifurcation analysis for the suggested predator-prey model. Using the Routh-Hurwitz stability criterion and a suitable Lyapunov function, we derived necessary and sufficient conditions for the local and global stability of the proposed model's possible equilibrium points. Next, codimension-1 bifurcations such as saddle-node bifurcation and Hopf-bifurcating limit cycles are examined by utilizing Sotomayor's theorem and the Lyapunov number. Finally, numerical examples are solved to confirm the theoretical results.