Dynamique non linéaire du modèle neuronal de Hindmarsh-Rose et synchronisation

Nathalie Corson (1) , Moulay Aziz-Alaoui (1)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

This work adresses neuron mathematical models. The aim is first the understanding of the biological meaning of existing mathematical models concerning neurons such as Hodgkin-Huxley or Hindmarsh-Rose models. The local stability and the numerical asymptotic analysis of Hindmarsh-Rose model are then developed in order to comprehend the dynamic evolution of a single Hindmarsh-Rose neuron. This examination naturally leads to the study of neuron networks. The study of these networks uses the synchronization theory which shows the connexions between two neurons. This has been performed using numerical tools.

Domaines: Systèmes dynamiques [math.DS]

Nathalie Corson, Moulay Aziz-Alaoui. Dynamique non linéaire du modèle neuronal de Hindmarsh-Rose et synchronisation. 10e Rencontre du Non-Linéaire Paris 2007, Mar 2007, Paris, France. p. 31. ⟨hal-00952563⟩