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Linear stability of scroll waves.

H Henry1, V Hakim

  • 1Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France.

Physical Review Letters
|January 3, 2001
PubMed
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Linear stability analysis reveals that three-dimensional deformations significantly impact scroll wave dynamics in excitable media. Twist induces sproing instability in scroll waves above a critical threshold.

Area of Science:

  • * Computational physics and mathematical modeling.
  • * Nonlinear dynamics and pattern formation in reaction-diffusion systems.

Background:

  • * Scroll waves are crucial three-dimensional (3D) wave structures in excitable media, analogous to two-dimensional (2D) spiral waves.
  • * Understanding the stability of these waves is essential for comprehending phenomena like cardiac arrhythmias and neural signal propagation.
  • * Previous studies have explored 2D spiral dynamics, but the stability of 3D scroll waves, particularly their behavior in the third dimension, requires further investigation.

Purpose of the Study:

  • * To conduct a comprehensive linear stability analysis of straight scroll waves in an excitable medium.
  • * To investigate the role of five dominant eigenmode branches, corresponding to 3D deformations of 2D spiral modes, in scroll wave dynamics.
  • * To determine the influence of wave twist on stability and identify potential instabilities like the sproing instability.

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Main Methods:

  • * Full linear stability analysis applied to a straight scroll wave model.
  • * Identification and analysis of five key eigenmode branches governing 3D dynamics.
  • * Systematic investigation of the effects of third-dimensional modulations and wave twist on stability across different parameter regimes.

Main Results:

  • * Five eigenmode branches significantly influence scroll wave stability, reflecting 3D deformations of 2D spiral dynamics.
  • * For untwisted scroll waves, out-of-plane deformations can either stabilize or destabilize wave behavior depending on parameter values.
  • * Wave twist was found to induce deformation in translation branches, leading to the "sproing instability" above a specific twist threshold.

Conclusions:

  • * Three-dimensional deformations play a dominant role in the stability of scroll waves.
  • * The study partially validates and refines previous predictions regarding the effects of out-of-plane modulations.
  • * Wave twist is identified as a critical factor driving the sproing instability in scroll waves.