Stability Analysis And Hopf Bifurcation Of Predator-prey Model Based On Bazykin Functional Response

Population dynamics is an important part of research in the field of ecology.It includes the discussion of the interaction between populations.The interaction relationship between populations can usually be expressed by a function,which we call functionality Response function.Due to the different populations,functional response functions are also divided into many categories.Common functional response functions are Holling ?,Holling?,Holling?and Beddington type functional response functions.The main research in this article is to describe The Bazykin-type functional response function of the saturated destabilizing force of the predator and the stabilizing force of competing for prey.From the perspective of biological mathematics,this paper constructs a predator-prey model with Bazykin-type functional response due to the impact of disease.Thus,the biological population is divided into three categories,namely,predator,susceptible predator,and victim Infected predator.The article studies the constructed model,obtains four types of equilibrium points and uses Hurwitz criterion,constructing Lyapunov function and other methods to analyze the stability of the model.The results are numerically simulatedThen,considering realistic factors,in the fourth chapter,time delay is added to the established model,and the theoretical knowledge of time delay is used to analyze the equilibrium point and Hopf branch of the system with time delay,so as to obtain the conditions required to produce the Hopf branch.