Dynamics of the Discretized FitzHugh-Nagumo Equation

I will consider the FitzHugh-Nagumo PDE. It is well-known in neuroscience and is used to describe the propagation of voltage impulse through a nurve axion. Its discrete version provides a competing model that I discuss in the talk. I present some results on the dynamics of the evolution operator on the space of traveling wave solutions and in particular, show that this dynamics changes from Morse-Smale type to a chaotic attractor to a horseshoe as a leading parameter (corresponding to the Reynolds number) of the system varies.