具分段常数变量时滞造血模型的分支分析  

Bifurcation analysis of a time-delayed hematopoiesis model with piecewise constant variables

作　　者：陈斯养[1] 黄晓宇[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《华中师范大学学报（自然科学版）》2014年第2期153-161,共9页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(10871122;11171119);中央高校基本科研专项基金项目(GK201302004;GK201302006)

摘　　要：讨论了一类具分段常数变量时滞造血模型的分支问题.利用差分方程的特征值理论,得到模型局部渐近稳定的充要条件;依据分支理论,得到了模型的Neimark-Sacker分支及Flip分支的存在性条件;基于规范化理论及中心流形定理,研究了分支的方向及稳定性;通过举例与数值模拟验证了所得条件与结论的正确性与可实现性.A time-delayed hematopoiesis model with piecewise constant variables is discussed.Applying the eigenvalue theory and Jury criterion,the necessary and sufficient conditions for the local asymptotic stability of the system are obtained.By bifurcation theory,the conditions for the existence of Neimark-Sacker and Flip bifurcation are studied.The direction and stability of Neimark-Sacker and Flip bifurcation is investigated based on the normal form approach theory and center manifold theory.Finally the feasibility of the conditions and conclusions is illustrated by some examples and simulations.

关 键 词：分段常数变量 局部渐近稳定 Flip分支 Neimark-Sacker分支 

分 类 号：O175.7[理学—数学]