Classification of wave regimes in excitable systems with linear cross-diffusion

M. A. Tsyganov, V. N. Biktashev,

Submitted to PRE: 2014/07/04. First revision: 2014/08/15. Second revision: 2014/11/07. Accepted: 2014/11/25. Published as PRE 90:062912, 2014/12/12

We consider principal properties of various wave regimes in two selected excitable systems with linear cross-diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope waves, multi-envelope waves, and intermediate regimes appearing as waves propagating fixed-shape most of the time but undergoing restructuring from time to time. Depending on parameters, most of these regimes can be with and without the ``quasi-soliton'' property of reflection of boundaries and penetration through each other. We also present some examples of behaviour of envelope quasi-solitons in two spatial dimensions.

Published version: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.062912