Skip to main content
SpringerLink
Log in
Book cover

Chaos in Biological Systems pp 19–22Cite as

Bifurcations in a Model of the Platelet Regulatory System

  • Chapter

Part of the book series: NATO ASI Series ((NSSA,volume 138))

Abstract

Modelling of the control mechanism for the regulation of platelet production leads to a functional differential equation with two time delays, one accounting for the senescence time of platelets, and the other one due to the maturation time of megakaryocytes. Local stability analysis and numerical simulations are performed to evaluate the possible behaviours of the solutions as clinically relevant, physiologically realistic parameters are varied. In particular, possible mechanisms for the onset of cyclic thrombocytopenia and idiopathic thrombocytopenic purpura are discussed.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Bélair, “Stability of a differential-delay equation with two time lags”, CMS Proceedings, to appear (1987).

    Google Scholar 

  2. J. Bélair and M.C. Mackey, “Oscillatory pathologies of platelet control”, in preparation (1987).

    Google Scholar 

  3. I. BranehÖg, J. Kutti and A. Weinfeld, Brit. J. Haematol. 27: 127143 (1974).

    Google Scholar 

  4. T. Cohen and D.P. Cooney, Scand. J. Haematol. 12: 9–17 (1974).

    Article  PubMed  CAS  Google Scholar 

  5. L. Glass and M.C. Mackey, Ann. N.Y. Acad. Sci. 316: 214–235 (1979).

    Article  PubMed  CAS  Google Scholar 

  6. L.A. Harker, J. Clin. Invest. 48: 963–974 (1969).

    Article  PubMed  CAS  Google Scholar 

  7. L.A. Harker, Clin, in Haematol. 6: 671–693 (1977).

    CAS  Google Scholar 

  8. U. Miller, J. Kulina, J. Luber, H.-P. Hebestreit, M. Mayer, U. Kempgens and W. Quisser, Blut 34: 31–38 (1977).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de mathématiques et de statistique and Centre de recherches mathématiques, Université de Montréal, C.P. 6128, Succursale A, Montréal, Québec, H3C 3J7, Canada

    Jacques Bélair

Authors
  1. Jacques Bélair
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Odense University, Odense, Denmark

    H. Degn  & L. F. Olsen  & 

  2. The University of Leeds, Leeds, UK

    A. V. Holden

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer Science+Business Media New York

About this chapter

Cite this chapter

Bélair, J. (1987). Bifurcations in a Model of the Platelet Regulatory System. In: Degn, H., Holden, A.V., Olsen, L.F. (eds) Chaos in Biological Systems. NATO ASI Series, vol 138. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9631-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-9631-5_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9633-9

  • Online ISBN: 978-1-4757-9631-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation