Asymptotic dynamics of Hindmarsh-Rose neuronal system

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

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

This work adresses the asymptotic dynamics of a neuronal mathematical model. The aim is first the understanding of the biological meaning of existing mathematical systems 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 bifurcations and dynamics evolution of a single Hindmarsh-Rose neuron. This has been performed using numerical tools borrowed from the nonlinear dynamical system theory.

Mots clés: neuron model; asymptotic dynamics; bifurcation; chaos

Domaines: Systèmes dynamiques [math.DS]

Nathalie Corson, Moulay Aziz-Alaoui. Asymptotic dynamics of Hindmarsh-Rose neuronal system. Dynamics of Continuous, Discrete and Impulsive Systemes, Series B: Applications and Algorithms, 2009, 16, p.535. ⟨hal-00952598⟩