一类干扰血液模型的Hopf分支

Hopf Bifurcation of A General Hematopoiesis Model

研究了一类具有离散时滞和干扰的血液模型的Hopy分支周期解。利用函数的单调性,分支理论及周期函数正交性等方法得到了该模型正平衡态存在唯一的充要条件,分支周期解存在条件和近似表达式,举出实例且运用Matlab绘出了血液模型数值解的拟合图,并分析了参数对周期解的周期,振幅及正平衡态的影响。

The Hopf bifurcation periodic solution in a general hematopoiesis model with decrete delays and disturbs are discussed. The necessary and sufficient conditions of the existence and uniquity of the positive equlibria by applying functional derivative is obtained, bifurcation values for the existence of bifurcation periodic solution are derived and the form of the approximate periodic solution is obtained by using the solvability andition. Some specific examples are given and the solution diagrame appears by Matlab. The influence to period, swing, positive equilibrium of period solution are discussed. When parameters in the process of diversification.