Hopf bifurcation in a space dependent reaction-diffusion system of FitzHugh-Nagumo type
Benjamin Ambrosio

The Fitzhugh-Nagumo system is a reduction in two variables of the
Hodgkin-Huxley model for the dynamics of neuron membrane potential and
ionic conductances. By varying a parameter, the system can be either
excitable or oscillatory. The transition towards oscillatory regime occurs
trough an Hopf bifurcation. In this talk, I consider a reaction-diffusion
system of FitzHugh-Nagumo type obtained by adding a Laplacian term in the
first equation, and choosing a parameter dependent on the space variable.
This allows to obtain propagation of central oscillations by playing with a
parameter.  I will divide the talk in two parts: in the first part, I will
review the main characteristics of ODE system whereas in the second part I
will show the occurence of the Hopf bifurcation the reaction-diffusion