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Persistent tangled vortex rings in generic excitable media

A T Winfree1

  • 1Department of Ecology and Evolutionary Biology, University of Arizona, Tucson 85721.

Nature
|September 15, 1994
PubMed
Summary

Turbulent tangles of vortex lines, not just symmetrical spirals, are a stable feature in excitable media. These complex structures, observed in numerical studies, are expected to appear in various biological and chemical systems.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Chemical Kinetics

Background:

  • Excitable media, found in biological systems (e.g., heart muscle) and chemical reactions (e.g., Belousov-Zhabotinsky reaction), exhibit wave propagation phenomena.
  • Activity patterns in these media often manifest as spiral waves originating from a central vortex.
  • In three-dimensional systems, these vortices form lines that can create stable, topologically classifiable structures like linked and knotted rings.

Purpose of the Study:

  • To investigate the general configuration of vortex lines in three-dimensional excitable media beyond previously studied symmetrical structures.
  • To determine the stability and robustness of these vortex line configurations under varying conditions.

Main Methods:

  • Numerical simulations of a generic excitable medium.
  • Analysis of vortex line configurations and their stability.
  • Perturbation analysis to test robustness against parameter changes.

Main Results:

  • The study reveals that the more general configuration of vortex lines in excitable media is a turbulent tangle.
  • This turbulent tangle configuration is robust against changes in system parameters and external perturbations.
  • Unlike previously identified symmetrical vortex structures, the turbulent tangle represents a more general and stable organizing center.

Conclusions:

  • Turbulent tangles of vortex lines are a stable and general feature of three-dimensional excitable media.
  • These structures are expected to be observable in a wide range of known excitable systems due to their inherent stability.
  • The findings challenge the exclusive focus on symmetrical vortex structures and highlight the prevalence of complex, turbulent organization.

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