与脑乳酸动力学相关的快-慢系统中的浸渍和缓冲
Dip and Buffering in a fast-slow system associated to Brain Lactacte Kinetics
摘要：
高维分区动力系统已被引入到大脑代谢的模型。本文提出了一种数学分析的方法。这些模型的减少是通过用控制项代替几个隔间来获得的。分析集中在乳酸动力学。可以提出对在刺激下观察到的乳酸的初始下降和周期性缓冲的数学分析，所述周期性缓冲是对相同刺激的重复序列的响应的基础。这种数学分析依赖于时间多尺度动力系统的渐近技术，如沿慢流形平均。
英文摘要：
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.
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