Abstract:
In this talk, we focus on a network of reaction-diffusion systems of 
Hodgkin-Huxley type. After a brief background on the Hodgkin-Huxley 
model and the relevance of the network approach  in Neuroscience context, 
we will present more theoretical aspects. We give a general  mathematical 
framework  for the network, in which we prove existence and uniqueness 
of solutions as well as  existence of invariant regions and of the attractor. 
Then, we illustrate numerically bifurcation phenomena and propagation 
of bursting oscillations through one and two coupled non-homogeneous 
systems. This is a joint work with M.A. Aziz-Alaoui and A. Balti.