Dynamics Research Of Biological Model

Biological mathematics plays an important role for the production of human. Thebiological dynamics is an important branch of Mathematical Biology,are now widelyused to study the law of life science. Ecological dynamics uses the dynamics model todescribe the relationship between groups,organisms and their environment. People candeeply understand ecology and natural by researching model and controlling parame-ters.This first part introduces the commom population dynamic model.Firstlyintroduces the single population dynamic model of common two models.It thenintroduces the two population dynamical models and research the dynamic behavior ofthe model.Finally research the dynamic behavior of different kinds of functionalreaction system,The second part introduces the dynamic system of some of the basic.Firstlyintroduces the definition of dynamic system and equilibrium point,introduces thetopology state of different kinds of equilibrium point.Nextly introduces two kinds ofbasic bifurcation--fold bifurcation and Hopf bifurcation,mianly research generationconditions and property. Then introduces the definition of stable manifold and unstablemanifold theorem.Finally introduces center manifold theorem.The third part introduces dynamics of a predator-prey system with Holling-IIfunctional response. The system has threee quilibrium points. By normal form theoryand qualitative analysis of planar sysyem, the properties of equilibria under variousparameter values are obtained. They can be saddle, stable node, saddle-node, unstablenode and weak focus. By the first Lyapunov number, the supercriticsl and subcriticalHopf bifurcations are discussed. The numerical simulations verify the above results.Based on the system dynamic analysis,know the conversion rate of predator m is greaterthan1,the rate of prey b tends to b0.When b acrosses b0,the system can produce a stablelimit cycle,this can proof the predator and prey can live forever by the form of stabilityperiodic solution.So this paper uses the dynamics method to illustrate life science ofHolling-II functional response.