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In this paper, a two species amensalism model with Michaelis–Menten type harvesting and a cover for the first species that takes the form $$begin{aligned} u0026frac{dx(t)}{dt}=a_{1}x(t)-b_{1}x^{2}(t)-c_{1}(1-k)x(t)y(t)- frac{qE(1-k)x(t)}{m_{1}E+m_{2}(1-k)x(t)},  u0026frac{dy(t)}{dt}=a_{2}y(t)-b_{2}y^{2}(t) end{aligned}$$is investigated, where (a_{i}), (b_{i}), (i=1,2), and (c_{1}) are all positive constants, k is a cover provided for the species x, and (0u003c ku003c1). The stability and bifurcation analysis for the system are taken into account. The existence and stability of all possible equilibria of the system are investigated. With the help of Sotomayor’s theorem, we can prove that there exist two saddle-node bifurcations and two transcritical bifurcations under suitable conditions.

Stability and bifurcation analysis of two species amensalism model with Michaelis–Menten type harvesting and a cover for the first species