Dynamical Analysis And Numerical Simulations For Two Nonlinear Food Chain Models

In this paper,the dynamic behavior of now two kinds of prey-predator-top predator food chain models with non-monotonic functional responses are studied.Two important thresholds,namely the top predator extinction threshold and the coexistence threshold are deduced,which play an important role in characterizing the dynamic behavior of the models.Firstly,the nutrient conversion rate of the predator to the top predator is analyzed,and and the relationship among prey,predator and higher predator is expressed by the nutrient conversion rate.the nonlinear predator harvesting of the top predator is dis-cussed,and the extinction,permanence of the top predator and bistable conditions are obtained by selecting the appropriate threshold.Secondly,the local asymptotic stabili-ty of the equilibria are proved by using Routh-Hurwitz criterion and relevant theorems.and the bifurcation theory of ordinary differential equations,central manifold theory and Sotomayor theorem are used to discuss the saddle-node bifurcation and the Hopf bifur-cation of the two kinds of models.Finally,the theoretical analysis results are verified by numerical simulation,and the dynamic behaviors of the two models are shown.