Linear Stability of Scroll Waves

Abstract

A full linear stability of a straight scroll wave in an excitable medium is presented. The five eigenmode branches which correspond to deformation in the third dimension of the five main modes of two-dimensional (2D) spiral dynamics are found to play a dominant role. Modulations in the third dimension have stabilizing or destabilizing effects on the different modes depending on the parameter regimes. For untwisted scroll waves, our numerical results confirm the relation between the long-wavelength behavior of the translation branches and 2D spiral drift in an external field but show no similar direct relation for the meander branches. The influence of twist on the different branches is investigated. In particular, the sproing instability is seen to arise from the twist induced deformation of the translation branches above a threshold twist.

5 pages 4 figures, to appear in Physical Review Letters

References in corpus (5)

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• The dynamics of vortex lines in the three-dimensional complex Ginzburg-Landau equation: instability, stretching, entanglement, and helices
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Cited by in corpus (5)

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• Effective dynamics of twisted and curved scroll waves using virtual filaments
• Dynamics of Pulsed Flow in an Elastic Tube