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

作　　者：Suqi Ma Suqi Ma(Department of Mathematics, China Agricultural University, Beijing, China)

机构地区：[1]Department of Mathematics, China Agricultural University, Beijing, China

出　　处：《International Journal of Modern Nonlinear Theory and Application》2021年第1期13-27,共15页现代非线性理论与应用（英文）

摘　　要：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.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.

关 键 词：State Feedback Control Time Delay Hopf Bifurcation 

分 类 号：O17[理学—数学]