Bulletin of Mathematical Biology

, Volume 81, Issue 10, pp 4251–4270 | Cite as

Analysis of a Mathematical Model for the Glutamate/Glutamine Cycle in the Brain

  • A. Perrillat-Mercerot
  • N. Bourmeyster
  • C. Guillevin
  • A. MiranvilleEmail author
  • R. Guillevin
Original Article


Our aim in this article is to study the well-posedness and properties of a system with delay which is related with brain glutamate and glutamine kinetics. In particular, we prove the existence and uniqueness of nonnegative solutions. We also give numerical simulations and compare their order of magnitude with experimental data.


Brain glutamate/glutamine cycle Substrate kinetics System with delay Regularity Well-posedness Linear stability Simulations 

Mathematics Subject Classification

34A34 35B09 35Q92 



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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Applications, UMR CNRS 7348, SP2MI, Equipe DACTIM-MISUniversité de PoitiersChasseneuil Futuroscope CedexFrance
  2. 2.Laboratoire Signalisation et Transports Ioniques Membranaires, ERL CNRS 7003, Equipe 4CS, CHU de PoitiersUniversité de PoitiersPoitiersFrance
  3. 3.CHU de PoitiersPoitiersFrance

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