Bifurcation Analysis Of Predator-prey Diffusive Model With Multiple Factors

This paper studies a new predator-prey diffusive model,which mainly considers the effect of additional food,prey refuge and the fear of prey on the predator's predation be-havior on the model population dynamics behavior.Firstly,we study the local stability of the equilibria,the boundedness and positivity of the solutions,and the existence of limit cycles of the corresponding ordinary differential system.Secondly,we make a priori esti-mation of the model and obtain the value range of the non-negative non-trivial solutions,and prove that there is no non-negative non-trivial solution when the diffusion coefficients of both predator and prey are greater than the threshold d*.At the same time,the result demonstrates that the Turing branch does not appear at the positive equilibrium point.Finally,we consider the existence of the Hopf branches at the positive equilibrium point.Further,this paper explores the direction and stability of the Hopf branches by means of the central manifold theorem as well as the Poincar(?) normal form theory.In addition,the existence of the steady-state branches at the positive equilibrium point is also studied,and three cases in which Hopf branches and steady-state branches occur simultaneously are shown by numerical examples.