Dynamic Analysis Of Several Biological Mathematical Models

This paper studies dynamics of several biological mathematical models and analyzes the basic properties of models,the existence and stability of equilibria and bifurcation phenomenon.The first chapter is the introduction of research background,actuality and the main work of this paper.The second chapter mainly studies dynamics of a Leslie-Gower predator-prey model with prey population subject to Allee effect.The positive invariance of the model and existence and stability of equilibria are analyzed.The sufficient conditions for global asymptotical stability of the interior equilibrium are obtained using Lyapunov stability theory.Further the existence of Hopf bifurcation,direction and stability of the limit cycle bifurcating from Hopf bifurcation are also discussed.The third chapter mainly studies dynamics of an eco-epidemiological model with Beddington-DeAngelis functional response and disease in the prey population subject to Allee effect.The positive invariant region of the model and existence of equilibria are obtained.The stability of equlibria is analyzed by the Routh-Hurwitz criterion and center manifold theorem.And the bifurcation phenomenon around the interior equilibrium is discussed,which shows the influence of the disease transmission rate,Allee effect and emergent carrying carrying on the model.In chapter four,dynamics of the NF-?B signalling model are researched.The positive invariant region of the model and existence and uniqueness of equilibrium are obtained.The local and global asymptotic stability of the interior equilibrium are analyzed by the Routh-Hurwitz criterion and second additive composition matrix.And the Hopf bifurcation phenomenon is also discussed.The fifth chapter is the conclusion of this paper.