Quasi-harmonic rotating waves in distributed active systems

Abstract

This paper concerns the rotating wave patterns in active media simulated by a two-component nonlinear system of parabolic equations. Three types of rotating waves are analysed: reverberators (Archimedean spirals), logarithmic spirals, and vortices in the form of rotating straight lines. It is found that only reverberators, which are of particular interest in biophysical applications, exist in active media with linear or nonlinear dispersion. Logarithmic spirals and vortices occur in the media without dispersion. The dependences of the characteristics of a rotating wave on its topological charge and on the parameters of the active medium are investigated in a quasi-harmonic approximation in the Fitz-Hugh-Nagumo and the λ-ω models. The stability condition of the vortices with a multiple topological charge in the λ-ω systems is found.