Imperfect bifurcation in predator–prey model with stocking and harvesting

In this paper, the imperfect and Bogdanov–Takens bifurcations are investigated in a Leslie–Gower predator–prey model with constant stocking and harvesting. It is shown that the introduction of the stocking of predators can prompt the extinction of prey; with the harvesting of predators, the model will experience the imperfect bifurcation and the Bogdanov–Takens bifurcation; meanwhile, no such bifurcations occur in the model with the stocking. The results imply that human intervention may lead to complex dynamical phenomena among species. Numerical simulations are presented to illustrate the theoretical results.