Numerical Modeling of Coexistence, Competition and Collapse of Rotating Spiral Waves in Three-Level Excitable Media with Discrete Active Centers and Absorbing Boundaries

TL;DR

This study numerically investigates the complex behaviors of rotating spiral waves in three-level excitable media with discrete active centers and absorbing boundaries, revealing new phenomena like nonlinear reflections and multiple wave births.

Contribution

It introduces a generalized three-level model for excitable media, uncovering novel spiral wave dynamics influenced by a second diffusion channel and boundary interactions.

Findings

Discovery of nonlinear 'reflections' of spiral waves at boundaries

Observation of multiple new spiral wave formations near boundaries

Identification of unique core evolution mechanisms leading to wave persistence

Abstract

Spatio-temporal dynamics of excitable media with discrete three-level active centers (ACs) and absorbing boundaries is studied numerically by means of a deterministic three-level model (see S. D. Makovetskiy and D. N. Makovetskii, on-line preprint cond-mat/0410460 ), which is a generalization of Zykov- Mikhailov model (see Sov. Phys. -- Doklady, 1986, Vol.31, No.1, P.51) for the case of two-channel diffusion of excitations. In particular, we revealed some qualitatively new features of coexistence, competition and collapse of rotating spiral waves (RSWs) in three-level excitable media under conditions of strong influence of the second channel of diffusion. Part of these features are caused by unusual mechanism of RSWs evolution when RSW's cores get into the surface layer of an active medium (i.~e. the layer of ACs resided at the absorbing boundary). Instead of well known scenario of RSW collapse, which takes place after collision of RSW's core with absorbing boundary, we observed complicated transformations of the core leading to nonlinear ''reflection'' of the RSW from the boundary or even to birth of several new RSWs in the surface layer. To our knowledge, such nonlinear ''reflections'' of RSWs and resulting die hard vorticity in excitable media with absorbing boundaries were unknown earlier. ACM classes: F.1.1, I.6, J.2; PACS numbers: 05.65.+b, 07.05.Tp, 82.20.Wt