一类造血模型的全局渐近性及Hopf分支周期解  

The global asymptoticy and Hopf bifurcation in a hematopoiesis model with delay

作　　者：田亚品[1] 陈斯养[1] 

机构地区：[1]陕西师范大学数学与信息科学学院

出　　处：《安徽大学学报（自然科学版）》2007年第6期19-23,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10071048);陕西师范大学重点科研基金资助项目(995091)

摘　　要：研究了一类具有离散时滞的造血模型正平衡态的全局渐近性及Hopf分支周期解.利用函数导数的性质,构造Lyapunov函数的方法、分支理论及周期函数的正交性,分别在δ>0和δ=0的情况下得到了该模型正平衡态的存在唯一性的充要条件,全局吸引性的充分条件及分支周期解的存在性条件和近似表达式.举出实例,运用M atlab给出了血液模型的数值解的拟合图像.The global asymptoticy of the positive equlibria and hopf bifurcation peridic solution in a hematopoiesis model with decrete delays are studied. In δ 〉 0 and in δ = 0 , the necessary and sufficient conditions of the existence and uniquity of the positive equlibria by applying functional derivative is obtained, the global attractiveness of the positive equlibria is investigated by stucuring Lyapunov function and bifurcation periodic solution are derived and the form of the approximate peridic solution is obtained by using the solvability condition. Some specific examples are given and the solution diagrame appears by Matlab.

关 键 词：造血模型 周期解 全局渐近性 HOPF分支 

分 类 号：O175.7[理学—数学]