In this paper, a single-species model with distributed delay and non-monotonic harvesting function is considered. The single-species model is converted into a two-dimensional equivalent system by using an appropriate transformation. Applying qualitative theory for ordinary differential equations, we investigate the existence and stability of the equilibria of the two-dimensional system in different cases. Hopf bifurcation, Bogdanov-Takens bifurcation, saddle-node bifurcation and homoclinic bifurcation are also discussed by the bifurcation theory of ordinary differential equations. The main results are verified by numerical simulations.
Yang et al. (Tue,) studied this question.