Drift Laws for Spiral Waves on Curved Anisotropic Surfaces

Abstract

Rotating spiral waves organize spatial patterns in chemical, physical and biological excitable systems. Factors affecting their dynamics such as spatiotemporal drift are of great interest for par- ticular applications. Here, we propose a quantitative description for spiral wave dynamics on curved surfaces which shows that for a wide class of systems, including the BZ reaction and anisotropic cardiac tissue, the Ricci curvature scalar of the surface is the main determinant of spiral wave drift. The theory provides explicit equations for spiral wave drift direction, drift velocity and the period of rotation. Depending on the parameters, the drift can be directed to the regions of either maximal or minimal Ricci scalar curvature, which was verified by direct numerical simulations.

preprint before submission to Physical Review E

References in corpus (2)

• Spiral wave drift in an electric field and scroll wave instabilities
• Buckling of scroll waves

Cited by in corpus (7)

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• Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field
• Effective dynamics of twisted and curved scroll waves using virtual filaments
• Pro-arrhythmogenic effects of heterogeneous tissue curvature: A suggestion for role of left atrial appendage in atrial fibrillation
• A response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves
• Stability of patterns on thick curved surfaces
• Scroll Waves and Filaments in excitable Media of higher spatial Dimension