Journal of Evolution Equations

, Volume 14, Issue 4–5, pp 841–862 | Cite as

Delay equation formulation of a cyclin-structured cell population model

  • Ricardo Borges
  • Àngel Calsina
  • Sílvia Cuadrado
  • Odo Diekmann
Article

Abstract

The aim of this paper is to derive a system of two renewal equations from individual-level assumptions concerning a cyclin-structured cell population. Nonlinearity arises from the assumption that the rate at which quiescent cells become proliferating is determined by feedback. In fact, we assume that this rate is a nonlinear function of a weighted population size. We characterize steady states and establish the validity of the principle of linearized stability.

Mathematics Subject Classification

45D05 47D06 92D25 92C37 

Keywords

Delay equations Structured cell population Initial value problem Steady states Linearized stability principle 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Ricardo Borges
    • 1
  • Àngel Calsina
    • 1
  • Sílvia Cuadrado
    • 1
  • Odo Diekmann
    • 2
  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra (Barcelona)Spain
  2. 2.Department of MathematicsUtrecht UniversityUtrechtThe Netherlands

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