造血系统中的周期解分岔及反馈控制

Bifurcation of Periodic Solution of a Hematopological System and Feedback Control

摘要: 本文研究了一类基于粒子集落刺激因子管理嗜中性粒子的血液病振荡数学模型。通常造血系统内部过程由激发分化机制和成熟机制两部分组成。造血干细胞分化得到了动物和人类必须的三类血液细胞：白细胞、红细胞和血小板。文中应用DDE-Biftool软件，数值模拟了造血系统中的长周期解的周期解分叉，得到了周期解的倍周期分叉。倍周期分叉后系统出现混沌解，应用反馈控制可以消除混沌或把系统稳定在期望的轨道上。

Abstract: The oscillating phenomenon of a hematological cell model is investigated. Based on effective G-SCF administration, the mathematical blood cell model is described as DDEs with multi-delays. Com-monly, in blood cell models, the intrinsic mechanism is composed of triggering differentiating mechanism and maturation mechanism, and hematoplogical cell model differentiating into three types of necessary blood cells in the body. By applying numerical software DDE-Biftool, the bifur-cation of periodic solutions with long period are derived, and the period doubling bifurcation of periodic solutions is found at critical values. Chaotic solutions also appear afterwards period- doubling bifurcation, and the stabilization of dynamical chaos to the expected periodic solution is finished successfully by applying Pyragas feedback control method.