Dynamics Analysis Of A Three Species Food Chain Model With Beddington-Deangelis Functional Response

In nature,predation is a common phenomenon.Among them,the threespecies food chain model which is the basic building block of large-scale ecosystem has attracted wide attention.In this paper,we formulate a mathematical model to study the complex dynamical behavior of a three species food chain model with Beddington-DeAngelis functional response under the homogeneous Neumann boundary condition.First of all,the maximum principle and Gronwall inequalities are used to give the boundedness.Next,the conditions of the existence of constant equilibrium have been given,the local stability of constant equilibrium points is analyzed by the eigenvalue theory,and the global stability of constant equilibrium is proved by constructing Lyapunov function.Then,the upper bounds of positive steady state solutions is investigated by applying comparison and the maximum principle,and nonexistence of non-constant steady state solutions is discussed by applying the Poincare inequalities.What’s more,we show the existence of periodic orbit by the Hopf bifurcation theorem,the local structure of the bifurcation solution from the semi-trival solution is proved by the local bifurcation theorem.Finally,some numerical simulations are performed to illustrate the theoretical analysis.