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

TL;DR

This paper investigates various wave regimes in excitable systems with linear cross-diffusion, identifying different wave behaviors and properties, including quasi-solitons, across one and two spatial dimensions.

Contribution

It provides a detailed classification of wave regimes in excitable systems with linear cross-diffusion, highlighting the conditions for different wave behaviors and the presence of quasi-solitons.

Findings

Identification of fixed-shape, envelope, and multi-envelope waves.

Discovery of intermediate regimes with restructuring behavior.

Examples of envelope quasi-solitons in two dimensions.

Abstract

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.