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Tension of organizing filaments of scroll waves. (English) Zbl 0862.92002
Summary: We consider the asymptotic theory for the dynamics of organizing filaments of three-dimensional scroll waves. For a generic autowave medium where two-dimensional vortices do not meander, we show that some of the coefficients of the evolution equation are always zero. This simpler evolution equation predicts a monotonic change of the total filament length with time, independently of initial conditions. Whether the filament will shrink or expand is determined by a single coefficient, the filament tension, that depends on the medium parameters. We illustrate the behaviour of scroll wave filaments with positive and negative tension by numerical experiments. In particular, we show that in the case of negative filament tension, the straight filament is unstable, and its evolution may lead to a multiplication of vortices.

MSC:
92C05 Biophysics
92B05 General biology and biomathematics
35K57 Reaction-diffusion equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
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