In the paper, a predator-prey system with Beddington-DeAngelis functional response and constant rate harvesting is considered. Various dynamical behaviors of the system including saddle-node points and a cusp of codimension 2 are investigated by using the analysis of qualitative method and bifurcation theory. Also, it is shown that the system undergoes several kinds of bifurcation such as the saddle-node bifurcation, the subcritical and supercritical Hopf bifurcation, Bogdanov-Takens bifurcation by choosing the death rate of the predator and the harvesting rate of the prey as the bifurcation parameters. Some numerical examples are illustrated in order to substantiate our theoretical results. These results unveil far richer dynamics compared to the system without harvesting
