Global Dynamics of a Piecewise Smooth System for Brain Lactate Metabolism

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 Ca...

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Bibliographic Details
Published in:	Qualitative theory of dynamical systems Vol. 18; no. 1; pp. 315 - 332
Main Authors:	Françoise, J.-P., Ji, Hongjun, Xiao, Dongmei, Yu, Jiang
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 02-04-2019 Springer Nature B.V SP Birkhäuser Verlag Basel
Subjects:	Blood flow Brain Capillary flow Difference and Functional Equations Dynamical Systems Dynamical Systems and Ergodic Theory Mathematics Mathematics and Statistics Metabolism Orbits Qualitative analysis 37N25 Piecewise smooth system Modeling 34D20
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Summary:	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.
ISSN:	1575-5460 1662-3592
DOI:	10.1007/s12346-018-0286-z