The Persistence of Invasion and Diffusion Model of Poisonous Weeds with Allee Effect

In this paper, a water resource competition model of poisonous weed invasion and diffusion with Allee effect was studied. We first discuss the persistence of the model. After that, by discretizing the model, the population dynamics with and without Allee effect was simulated. The results shows that: 1. The Allee effect make it more difficult to reach persistence coexistence of edible grass and poisonous weeds; 2. The Allee effect leads to the dynamic change of population quantity from periodic coexistence to stability of poisonous weeds reaches saturation and edible grass becomes extinction.