关键词: 捕食者-食饵模型, Michaelis-Menten型收获, 替代性食饵, Hopf分支, 稳定性

Abstract: We considered a predator-prey model with alternative prey and Michaelis-Menten type harvesting. Firstly, we discussed the existence and stability of its boundary equilibrium points and interior equilibrium points. Secondly, taking the coefficient of Michaelis-Menten type harvesting as the bifurcation parameter, we proved the existence of Hopf bifurcation at its interior equilibrium point and its properties by using the Hopf bifurcation theorem. Finally, we verified the correctness of the theoretical results through numerical simulations by using MATLAB software.

Key words: predator-prey model, Michaelis-Menten type harvesting, alternative prey, Hopf bifurcation, stability