Spiral waves within a bistability parameter region of an excitable medium

V S Zykov,E Bodenschatz

doi:10.1088/1367-2630/ac47ca

Abstract

Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and ‘negative’ cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or ‘negative’ core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

Highlights

Wave processes in active media have attracted a great deal of attention in recent decades
The direct computations performed with the Barkley model clearly show that the spiral waves exist in a much wider parameter range than it was previously postulated by Alonso et al [26]
Our calculations clearly show that in the region of bistability parameters, spiral waves either rotate around the wave core, which is at rest, or the tip trajectory rotates around the ‘negative’ core, which is in an excited state

Summary

Introduction

Wave processes in active media have attracted a great deal of attention in recent decades. In figure 4(a), the parameter a corresponds to the left edge of the existence region, where the radius of a spiral wave core approaches infinity. The repetition of these computations for different values of b makes it possible to determine the boundaries of the region in which the spiral waves exist, indicated in figure 3 by the lines of triangles and diamonds.

Results

Conclusion