Bifurcation analysis of a single-species model with distributed delay and non-monotonic harvesting function

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.