Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2000-11-15
Phys. Rev. Lett. 85 5328-5331 (2000)
Nonlinear Sciences
Pattern Formation and Solitons
5 pages 4 figures, to appear in Physical Review Letters
Scientific paper
10.1103/PhysRevLett.85.5328
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.
Hakim Vincent
Henry Herve
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