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

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.