The stability analysis of brain lactate kinetics

Jean-Pierre Françoise; Hongjun Ji

doi:10.3934/dcdss.2020182

Article Contents

2020, Volume 13, Issue 8: 2135-2143. Doi: 10.3934/dcdss.2020182

This issue Previous Article From conservative to dissipative non-linear differential systems. An application to the cardio-respiratory regulation Next Article Gevrey solutions of singularly perturbed differential equations, an extension to the non-autonomous case

The stability analysis of brain lactate kinetics

Jean-Pierre Françoise^1, , and
Hongjun Ji^2,

1.
Université P.-M. Curie, Paris 6, Laboratoire Jacques–Louis Lions, UMR 7598 CNRS, 4 Pl. Jussieu, Tour 16-26, 75252 Paris, France
2.
Shanghai Jiao Tong University, SJTU-ParisTech Elite Institute of Technology, 800 Dong Chuan Road, 200240 Shanghai, China

^* Corresponding author: Jean-Pierre Francoise
^* Corresponding author: Jean-Pierre Francoise

Received: December 31, 2018

Early access: November 2019

Published: May 2020

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Abstract

Our aim in this article is to study properties of a generalized dynamical system modeling brain lactate kinetics, with $ N $ neuron compartments and $ A $ astrocyte compartments. In particular, we prove the uniqueness of the stationary point and its asymptotic stability. Furthermore, we check that the system is positive and cooperative.

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Mathematics Subject Classification: Primary: 34D20; Secondary: 37N25.

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References

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