Abstract: Based on a three-dimensional predator-prey model, we discussed the cooperation between prey populations and their impact on the predation process. Firstly, we analyzed the existence and stability of equilibrium points of the system by using dynamical system theory, and proved the periodic oscillation characteristics of equilibrium points in prey free populations. Secondly, the theoretical results were verified through numerical simulation. The numerical simulation results show that the equilibrium point E₁ of the prey free populations y and the equilibrium point E₂ of the prey free populations z are both periodic oscillations, and the amplitude of the oscillations gradually increases with the increase of the cooperative effect.

Key words: predator-prey model, cooperation, equilibrium point, numerical simulation