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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