Stability and Bifurcation Analysis of a Type of Hematopoietic Stem Cell Model

Suqi Ma
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引用次数: 2

Abstract

The observed dynamical property illustrates that state feedback control may stabilize invariant attractor to stable state in a simple version of hematopoietic stem cell model. The stability character of the positive steady state is analyzed by the computation of the rightmost characteristic roots in complex plane. Hopf bifurcation points are tracked as the roots curve crossing imaginary axis from the left half plane to the right half plane continuously. The bifurcation direction and stability of the bifurcating periodical solution are discussed by norm form computation combined with the center manifold theory. Furthermore, the numerical simulation verifies that instead of chaos, system is stabilized to period-1, 2, 3, 4 and period-7 periodical solutions in some delay windows, and the continuous of periodical solutions is also numerical simulated with varying free parameters continuously.
一类造血干细胞模型的稳定性和分岔分析
观察到的动力学特性说明状态反馈控制可以使一个简单版本的造血干细胞模型的不变量吸引子稳定到稳定状态。通过复平面上最右特征根的计算,分析了正稳态的稳定性特性。Hopf分岔点以根曲线从左半平面连续穿过虚轴向右半平面跟踪。通过范数形式计算,结合中心流形理论,讨论了分岔周期解的分岔方向和稳定性。此外,数值仿真验证了系统在某些延迟窗内稳定为周期1、周期2、周期3、周期4和周期7解而不是混沌,并对周期解的连续变化进行了数值模拟。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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