  High-dimensional compartmental dynamical systems have been introduced to
model brain metabolism. In this article, an approach is proposed to their
mathematical analysis. Reductions of these models are obtained by replacing
several compartments by a control term. The analysis focuses here on lactate
kinetics. A mathematical analysis of the initial dip of lactacte, observed
under stimulation, and of the periodic buffering, underlying the re- sponse to
a repetitive sequence of identical stimuli, can be proposed. This mathematical
analysis relies on asymptotics techniques of time multi-scaled dynamical
systems such as averaging along slow manifolds.

Dynamical Systems;Neurons and Cognition