Analysis Of Dynamic Stability Of Two Types Of Three Species Predator-Prey Model

In the study of ecosystems,populations are a typical type of complex system.Through the analysis of big data by biologists,we can build models for this and obtain the nonlinear dynamic equations of the ecosystem.According to the equations we have established,we analyze the existence of equilibrium points and the stability of equilibrium points,study the possibility of bifurcation at the equilibrium points in the three-group ecosystem,and finally verify the above analysis through computer simulation.The stability of ecosystem dynamics among the three populations.A study in this article is based on the traditional two-predator-one-prey model.We have made practical improvements to this,adding a one-way predation between the two predators.For example,eagles and snakes will both catch rabbits.For food,at the same time,eagles will also prey on snakes in some cases.At the same time,Holling-Ⅱ type functional response function is used in the model to describe the interaction between predator and prey.The model is analyzed and simulated.The existence and stability of equilibrium points under different parameter conditions.Considering that certain factors in the ecosystem will affect the stability of the population.When one of these influencing factors changes,it may cause dramatic changes in the diversity of species in the ecosystem,and even lead to the extinction of certain species in the ecosystem.In order to prevent this from happening,another of our work is to study one of the factors-the helping effect between the two prey,and we judge the impact on the prey by changing the Allee effect threshold,and verify it through numerical simulations.In the end,we found that increasing the help coefficient of a prey can promote the survival of oneself and improve the stability of the ecosystem;if the help of other prey is increased,it will have an adverse effect on oneself and reduce one’s own survival,even lead to its extinction.The main chapters of the article are as follows:The first chapter introduces research background and the basic knowledge and theories required.The second chapter analyzes the influence and stability on the dynamics of the Holling-Ⅱthree-group model.The third chapter explores the dynamic performance of two predators-one predator with help and Allee effect.