Qualitative Study On Several Types Of Cannibalistic Phase Structural Models With Density Constraints

Cannibalism is not uncommon in nature.It is a predator relationship that exists within a single population.Cannibalism often occurs between different stages of the same population.In most cases,larger individuals prey on smaller individuals.This phenomenon affects the dynamic behavior of the population system to varying degrees.In nature,the number of populations will not grow indefinitely due to density constraints.Therefore,it is more in line with natural phenomena to consider density constraints when studying cannibalistic populations with a stage structure.Based on the existing research results,this paper simulates natural phenomena and considers that adult individuals will increase the reproduction rate due to cannibalism,and the increased reproduction rate will be restricted by the number of juvenile individuals.Three types of adult predation with density constraints are established.Structural model of the infancy stage.The full article is divided into six chapters,and three types of models are analyzed.The main contents are as follows:In this article,we first established a type of ordinary differential equation model with a two-stage structure with density-dependent terms,and the adult predated the juvenile in the model.The system analyzes the conditions for the model to survive in the ecosystem and the existence of the equilibrium point;uses the central popular theorem to prove the stability of the equilibrium point,obtains the conditions for the model to produce saddle node branches,and shows that the model does not have a periodic solution;Numerical simulation supports the correctness of the analysis results.Secondly,on the basis of the constructed two-stage structure cannibalism model,a three-stage structure cannibalism model with density constraints is proposed,which further assumes that there are elderly individuals in the population.Firstly,the boundedness of the model solution is judged.In the bounded area,the Cartesian principle is used to judge the existence of the equilibrium point of the model;then the Routh-Hurwitz criterion and the two additive coincidence matrix are used to prove that there is an extinction equilibrium point and the only survival The global asymptotic stability of the equilibrium point is used.Sotomayor's theorem is used to analyze the condition of the saddle node branch of the system when there are two surviving equilibrium points.Finally,the correctness of the analytical results of the model dynamics theory is verified by numerical simulation.Finally,on the basis of the established two-stage structure cannibalism model,a kind of density-constrained adult predator juvenile stage structure delay model is established.The model further considers that reproduction is not completed in an instant,but a natural process of gestation.First,analyze the non-negativity of the model solution and the existence of the equilibrium point;then use the Lyapunov-Krasovski function to analyze the stability of the equilibrium point,and the condition of the Hopf branch of the model when there is a periodic solution,and discuss the branch of ?;finally,numerical simulations were carried out on the dynamics of the model.