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Global Dynamics of a Piecewise Smooth System for Brain Lactate Metabolism

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Abstract

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.

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Acknowledgements

This work was supported by the National Natural Science Foundations of China (N\(^\circ \) 11431008 and 11771282) and the NSF of Shanghai (N\(^\circ \) 15ZR1423700).

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Authors and Affiliations

  1. Laboratoire Jacques–Louis Lions, UMR 7598 CNRS, Université P.-M. Curie, Paris 6, 4 Pl. Jussieu, 16-26, 75252, Paris, France

    J.-P. Françoise & Hongjun Ji

  2. School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District, Shanghai, 200240, People’s Republic of China

    J.-P. Françoise, Dongmei Xiao & Jiang Yu

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  1. J.-P. Françoise
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  2. Hongjun Ji
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  3. Dongmei Xiao
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  4. Jiang Yu
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Correspondence to J.-P. Françoise.

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Françoise, JP., Ji, H., Xiao, D. et al. Global Dynamics of a Piecewise Smooth System for Brain Lactate Metabolism. Qual. Theory Dyn. Syst. 18, 315–332 (2019). https://doi.org/10.1007/s12346-018-0286-z

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  • DOI: https://doi.org/10.1007/s12346-018-0286-z

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