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We discuss the stability and bifurcation analysis for a predator-prey systemwith non-linear Michaelis-Menten prey harvesting. The existence and stabilityof possible equilibria are investigated. We provide rigorous mathematicalproofs for the existence of Hopf and saddle node bifurcations. We prove thatthe system exhibits Bogdanov-Takens bifurcation of codimension two, calculatingthe normal form. We provide several numerical simulations to illustrate ourtheoretical findings.

Bifurcations of a Leslie Gower predator prey model with Holling type III functional response and Michaelis-Menten prey harvesting