Section: New Results

Signal propagation along excitable chains

Participant : Arnaud Tonnelier.

Nonlinear self-sustained waves, or autowaves, have been identified in a large class of discrete excitable media. We have proposed a simple continuous-time threshold model for wave propagation in excitable media. The ability of the resulting transmission line to convey a one-bit signal is investigated. Existence and multistability of signals where two successive units share the same waveform is established. We show that, depending on the connectivity of the transmission line, an arbitrary number of distinct signals can be transmitted. More precisely, we prove that, for a one-dimensional information channel with $n\mathrm{th}$-neighbor interactions, a $n$-fold degeneracy of the speed curve induces the coexistence of $2n$ propagating signals, $n$ of which are stable and allow $n$ distinct symbols transmission. The influence of model parameters (time constants, coupling strength and connectivity) on the traveling signal properties is analyzed. This work is almost finished and is going to be submitted.