Relaxation oscillations in a class of delay differential equations

A. C. Fowler, Michael C. Mackey

Research output: Contribution to journalArticlepeer-review

Abstract

We study a class of delay differential equations which have been used to model hematological stem cell regulation and dynamics. Under certain circumstances the model exhibits self-sustained oscillations, with periods which can be significantly longer than the basic cell cycle time. We show that the long periods in the oscillations occur when the cell generation rate is small, and we provide an asymptotic analysis of the model in this case. This analysis bears a close resemblance to the analysis of relaxation oscillators (such as the Van der Pol oscillator), except that in our case the slow manifold is infinite dimensional. Despite this, a fairly complete analysis of the problem is possible.

Original languageEnglish
Pages (from-to)299-323
Number of pages25
JournalSIAM Journal on Applied Mathematics
Volume63
Issue number1
DOIs
Publication statusPublished - Aug 2002
Externally publishedYes

Keywords

  • Chronic myelogenous leukaemia
  • Delay differential equations
  • Hematopoiesis
  • Relaxation oscillations
  • Stem cells

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