# American Institute of Mathematical Sciences

## The stability analysis of brain lactate kinetics

 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

Received  January 2019 Published  November 2019

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.

Citation: Jean-Pierre Françoise, Hongjun Ji. The stability analysis of brain lactate kinetics. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020182
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