Hopf Bifurcation Of A Class Can Interfere With Blood Model And Asymptotic Of Neutral Impulsive Differential Equations,

The time delay and the interference of external have more influence and effective control on population density for most species in ecology. Impulsive on the biological effects of population rise to more and more attention of scholars at the present stage. Theory of Impulsive Differential Equations have not only improved the theory of differential equations but also provide a better model in the biological and economic aspects. The Hopf bifurcation periodic solution in a hematopoiesis model with decrete delays and disturbs,the asymptotic behavior of a class of nonlinear neutral functional differential equations and the persistence of N species predator-prey food chain are investigated by using analysis method,the logarithmic norm,comparison principle,constructing Lyapunov functions and the bifurcation theory, including the global existence of solutions,local asymptotic stability of the solutions,Oscillation of the solutions,the asymptotic behavior of the solutions and the uniform persistence.Blood is the lifeline of the human body mainly.Then,the hemopoiesis of stem cells is a focus which the medical field pay close attention to. First, The Hopf bifur-cation periodic solution in a hematopoiesis model with decrete delays and disturbs is investigated on this basis. The necessary and sufficient conditions of the existence and uniquity of the positive equlibria by applying functional derivative is obtained,bifurcation values for the ex-istence of bifurcation periodic solution are derived and the form of the approximate periodic solution is obtained.Some specific examples are given andthe solution di-agrame appears by Matlab. The influence to period,swing,positive equilibrium of period solution are discussed.Various theories of non-impulsive differential equations has been extensively developed, but many theories and methods of impulsive differential equations makes the particularity of its development is still relatively slow. Lyapunov functionals play an important role in resolving the Population Dynamics of sustainability, stability and so on.Second, the asymptotic behavior of a nonlinear neutral functional differential equations with positive and negative coefficients is discussed by constructing Lya-punov functions. Given equation tends to a normal number of sufficient conditions and examples of conditions and conclusions of Theorem achievability. Sufficient conditions that solution tends to a normal number are given,and the cor-rectness of the conditions of the theorem is shown by example.Predator-prey model is one of the important phenomena between biological interactions in nature. Finally, The Persistence in N predator-prey population is investigated.Sufficient condition of persistence is obtained by using inequality valu-ation and comparison principle.