Section: New Results

Propagation in space-discrete excitable systems

Participant : Arnaud Tonnelier.

We introduce a simplified model of excitable systems where the response of an isolated cell to an incoming signal is idealized by a fixed pulse-shape function. When the total activity of the cell reaches a given threshold a signal is sent to its $N$ neighbors. We show that a chain of such excitable cells is able to propagate a set of simple traveling waves where the time interval between the firing of two successive cells remains constant. A comprehensive study is done for a transmission line with $N=2$ and $N=3$. It is shown that, depending on initial copnditions, the network may propagate traveling waves with different velocities. Some necessary conditions for multistationarity are derived for an arbitrary $N$.