On the characteristic equation \(\lambda =\alpha _{1}+(\alpha _{2}+\alpha _{3}\lambda )e^{-\lambda }\) and its use in the context of a cell population model

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• 作者：Odo Diekmann ; Philipp Getto ; Yukihiko Nakata
• 关键词：34K20 ; 37N25 ; 45D05 ; 65L03 ; 92D25
• 刊名：Journal of Mathematical Biology
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：72
• 期：4
• 页码：877-908
• 全文大小：1,273 KB
• 参考文献：Adimy M, Chekroun A Touaoula TM (2015) Age-structured and delay differential-difference model of hematopoietic stem cell dynamics, DCDS-B (to appear)
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• 作者单位：Odo Diekmann (1)
  Philipp Getto (2)
  Yukihiko Nakata (3)
  
  1. Mathematical Institute, University of Utrecht, Utrecht, The Netherlands
  2. TU Dresden, Fachrichtung Mathematik, Institut für Analysis, 01062, Dresden, Germany
  3. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Biology
  Applications of Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1416

文摘

In this paper we characterize the stability boundary in the \((\alpha _{1},\alpha _{2})\)-plane, for fixed \(\alpha _{3}\) with \(-1<\alpha _{3}<+1\), for the characteristic equation from the title. Subsequently we describe a nonlinear cell population model involving quiescence and show that this characteristic equation governs the (in)stability of the nontrivial steady state. By relating the parameters of the cell model to the \(\alpha _{i}\), we are able to derive some biological conclusions. Mathematics Subject Classification 34K20 37N25 45D05 65L03 92D25