Stability and bifurcation analysis in hematopoietic stem cell dynamics with multiple delays

Ying Qu, Junjie Wei, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


This paper is devoted to the analysis of a maturity structured system of hematopoietic stem cell (HSC) populations in the bone marrow. The model is a system of differential equations with several time delays. We discuss the stability of equilibria and perform the analysis of Hopf bifurcation. More precisely, we first obtain a set of improved sufficient conditions ensuring the global asymptotical stability of the zero solution using the Lyapunov method and the embedding technique of asymptotically autonomous semiflows. Then we prove that there exists at least one positive periodic solution for the n-dimensional system as a time delay varies in some region. This result is established by combining Hopf bifurcation theory, the global Hopf bifurcation theorem due to Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Trans. Amer. Math. Soc. 350 (1998) 47994838], and a continuation theorem of coincidence degree theory. Some numerical simulations are also presented to illustrate the analytic results.

Original languageEnglish (US)
Pages (from-to)2011-2024
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Issue number20-22
StatePublished - Oct 15 2010


  • Global asymptotical stability
  • HSCs
  • Hopf bifurcation
  • Positive periodic solution

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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