Asymptotic Dynamics for Slow-Fast Hindmarsh-Rose Neuronal System,

Dynamics of Continuous, Discrete and Impulsive Systems, series B, Vol. 16(4), pp. 535-549 (2009)

Corson N. and Aziz-Alaoui M.A.

Labo. of Applied Maths., EA 3821, Le Havre University, France.

Abstract :

This work adresses the asymptotic dynamics of a neuronal mathematical model. The aim is first the understanding of the biological meaning of existing math- ematical 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.

Keywords: neuron model, asymptotic dynamics, bifurcation, chaos.

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