Global Dynamics of a Piecewise Smooth System for Brain Lactate Metabolism

• J.-P. Françoise ^[1] ; Ji, Hongjun ^[2] ; Xiao, Dongmei ^[1] ; Jiang, Yu ^[1]
  1. [1] Shanghai Jiao Tong University

     Shanghai Jiao Tong University

     China

     
  2. [2] Vitebsk State University named after P.M. Masherov

     Vitebsk State University named after P.M. Masherov

     Bielorrusia

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 1, 2019, págs. 315-332
• Idioma: inglés
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• Resumen

  • 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.