  We discuss the stability and bifurcation analysis for a predator-prey system
with non-linear Michaelis-Menten prey harvesting. The existence and stability
of possible equilibria are investigated. We provide rigorous mathematical
proofs for the existence of Hopf and saddle node bifurcations. We prove that
the system exhibits Bogdanov-Takens bifurcation of codimension two, calculating
the normal form. We provide several numerical simulations to illustrate our
theoretical findings.
