Zeynab Lajmiri - Sama technical and vocational training college, Islamic Azad University Izeh Branch, Izeh, Iran.
Iman Orak - Sama technical and vocational training college, Islamic Azad University Izeh Branch, Izeh, Iran.
Reza Fereidooni - Research and development manager of oxin steel company of khozestan, Iran.

A predator-prey model was extended to include nonlinear harvesting of the predator guided by its population, such that harvesting is only implemented if the predator population exceeds an economic threshold. Theoretical results showed that the harvesting system undergoes multiple bifurcations, including fold, supercritical Hopf, Bogdanov-Takens and cusp bifurcations. We determine stability and dynamical behaviors of the equilibrium of this system. Numerical simulation results are given to support our theoretical results.

Hopf Bifurcation, Bogdanov-Takens bifurcation, Dynamical behavior, Cusp bifurcations