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Global Dynamics of a Piecewise Smooth System for Brain Lactate Metabolism

  • J.-P. Françoise
  • Hongjun Ji
  • Dongmei Xiao
  • Jiang Yu
Article
  • 21 Downloads

Abstract

In this article, we study a piecewise smooth dynamical system inspired by a previous reduced system modeling compartimentalized brain metabolism. The piecewise system allows the introduction of an autoregulation induced by a feedback of the extracellular or capillary Lactate concentrations on the Capillary Blood Flow. New dynamical phenomena are uncovered and we discuss existence and nature of two equilibrium points, attractive segment, boundary equilibrium and periodic orbits depending of the Capillary Blood Flow.

Keywords

Piecewise smooth system Qualitative analysis Modeling 

Mathematics Subject Classification

34D20 37N25 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundations of China (N\(^\circ \) 11431008 and 11771282) and the NSF of Shanghai (N\(^\circ \) 15ZR1423700).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • J.-P. Françoise
    • 1
    • 2
  • Hongjun Ji
    • 1
  • Dongmei Xiao
    • 2
  • Jiang Yu
    • 2
  1. 1.Laboratoire Jacques–Louis Lions, UMR 7598 CNRSUniversité P.-M. Curie, Paris 6ParisFrance
  2. 2.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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