Bifurcations and simulations of two predator–prey models with nonlinear harvesting.

Highlights • The nonlinear system has multiple internal equilibria. • Saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation may occur. • Heteroclinic and homoclinic orbit, bistability may appear. • Some numerical simulations are given. Abstract We propose and investigate a predator-prey model with selective nonlinear harvesting for the prey and predator, such harvesting increases smoothly to a limit value when the density of harvested population is large enough. The existence of nonlinear harvesting makes the dynamics of the model more complicated, including multiple equilibria, limit cycle, heteroclinic and homoclinic orbit, bistability, saddle-node bifurcation, transcritical bifurcation, subcritical and supercritical Hopf bifurcation and Bogdanov–Takens bifurcation. Furthermore, some numerical simulations are given to illustrate these results. [ABSTRACT FROM AUTHOR]