Propagation of bursting oscillations in coupled Hodgkin-Huxley non-homogeneous Reaction-Diffusion systems
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.