基于有限滞时的免疫系统的稳定性与分支解  

Stability and Solution of Hopf Bifurcation on a Class of Immune System with Finite Delay

作　　者：镇方雄[1] 刘三红[1] 肖氏武[2] 

机构地区：[1]咸宁学院数学与统计学院,湖北咸宁437100 [2]襄樊学院数学与计算机科学学院,湖北襄阳441053

出　　处：《襄樊学院学报》2011年第8期9-12,共4页Journal of Xiangfan University

基　　金：咸宁学院科研项目(ky09059)

摘　　要：以时滞τ为参数,利用特征根法分析平衡点的稳定性,得到稳定性存在的范围及在平衡点处产生hopf分支的条件,再利用中心流形定理和规范型理论,得到hopf周期解的稳定性及计算公式,为数值模拟提供依据.In this paper, using time lag τ as a parameter and using analytical method, we firstly analyze the stability and hopf bifurcation of the equilibriums in Marchuk＇s model. We obtain the condition and domain of stability on the equilibriums and the condition of the occurrence of hopf bifurcation. Secondly using the center manifold theorem and normal form theory, we obtain the calculation formulas which reflect the stability with hopf bifurcation periodic solution and bifurccation direction. Thus it provides a basis for numerical simulation calculation.

关 键 词：HOPF分支 中心流形 上临界分支 

分 类 号：O175.12[理学—数学]