Global Absorption, Two Types Of Hopf Bifurcation Of The Ecological Model And A Class Of Feedback Control Model

Ecological mathematics is one of the important branches of applied mathe-matics. Ecological mathematics solves biological problems through the mathemat-ical theory and studies the mathematical methods related with biology. The Hopf bifurcation of two ecological models and the global attractivity of a system with feedback controls dan delays are investigated in this paper, including the existence and uniqueness of the positive equilibrium state, the existence of the Hopf bifurca-tion, the stability of the positive equilibrium state and the global attractivity of the solution.Blood is the source of life. Reasonable hema.topoiesis models provide theoretical basises for the effective treatment of hematopoiesis diseases. First, the sufficient con-ditions of absolute stability and the conditions of the existence of Hopf bifurcation in a general hematopoiesis model with delays are investigated. Sufficient conditions of absolute stability are obtained by using the theory of the characteristic value. the conditions of the existence of Hopf bifurcation and the stability of model are given, and the feasibility of the main results is shown by the numerical simulations.The density of biological populations is the most basic quantitative character-istics of biological populations, which is affected by the delays and the interference of nature. On this basis, sufficient conditions of absolute stability and the existence of Hopf bifurcation in a Logistic model with delays and disturbs are investigated. Sufficient conditions of absolute stability and the existence of Hopf bifurcation are discussed in two different situations. Then fitted curve figures are presented by using Matlab and the effects of the parameters on bifurcation periodic solutions are discussed.In nature, the density of biological populations is also affected by the feedback controls. Global attractivity of a Logistic model with delays and feedback controls is investigated. The existence and uniqueness of the positive equilibrium are obtained by using the continuity of function, the boundeness of the solutions are obtained by using the method of constructing Lyapunov functional and the feasibility of the theoremes is shown by giving some examples.