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Periodic sequence of stabilized wave segments in an excitable medium.

V S Zykov1, E Bodenschatz1

  • 1Max Planck Institute for Dynamics and Self-Organization, D-37077 Goettingen, Germany.

Physical Review. E
|May 20, 2018
PubMed
Summary

Stabilizing periodic wave segments in excitable media requires specific parameter domains. A free-boundary approach reveals a constant parameter (H) at this domain

Area of Science:

  • Computational physics
  • Mathematical modeling
  • Nonlinear dynamics

Background:

  • Excitable media exhibit complex wave propagation phenomena.
  • Stabilization of periodic wave segments is crucial for understanding pattern formation.
  • Previous studies often relied on extensive numerical simulations.

Purpose of the Study:

  • To identify the conditions for stabilizing periodic wave segments in excitable media.
  • To introduce and analyze a key parameter (H) governing wave segment stability.
  • To validate a free-boundary approach against numerical simulations.

Main Methods:

  • Numerical computations of wave propagation in excitable media.
  • Application of a free-boundary approach to analyze parameter space.

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  • Utilizing the modified FitzHugh-Nagumo model for simulations.

    • Main Results:

    • Wave segment stabilization is confined to a restricted parameter domain.
    • A specific parameter (H) remains constant at the boundary of this domain.
    • This constant parameter (H) dictates wave propagation velocity and shape.

    Conclusions:

    • The free-boundary approach provides accurate predictions for wave segment behavior.
    • The identified parameter (H) is a critical determinant of wave stability and characteristics.
    • This work offers a more analytical understanding of wave stabilization in excitable media.