Advertisement

Applied Mathematics and Mechanics

, Volume 20, Issue 4, pp 418–425 | Cite as

The motion of organization center of scroll waves in excitable media with single diffusion

  • Liu Shenquan
  • Lu Qishao
  • Huang Kelei
Article

Abstract

The motion of organization center of three-dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear law are derived for untwisted organization center. These results have explicit physical meaning and are in good agreement with experiments

Key words

single diffusion scroll waves organization center vortex ring excitable media 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Winfree A T, Jahnke W. Three-dimensional scroll ring dynamics in the Belousov-Zabotinsky reagent and in the 2-variable Oregonator model [J].J Phys Chem, 1989,93: 2823–2832CrossRefGoogle Scholar
  2. [2]
    Tyson J J, Keener J P. The dynamics of scroll waves in excitable media [J].SIAM Review, 1992,34: 1–39MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Tyson J J, Keener J P. Singular perturbation theory of traveling waves in excitable media [J].Phys D, 1988,32: 327–361MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Welsh B J, Gomatam J, Burgess A E. Three-dimensional chemical waves in the Belousov-Zhabotinsky reagent [J].Nature, 1983, (304): 611–613CrossRefGoogle Scholar
  5. [5]
    Winfree A T, Stable particle-like solutions to nonlinear waves equations of three-dimensional excitable media [J].SIAM Review, 1990,32: 1–53MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Keener J P. The dynamics of three-dimensional scroll waves in excitable media [J].Phys D, 1988,31 (2): 269–276MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Keener J P. Knotted scroll waves filaments in excitable media [J].Phys D, 1989,34: 378–390MATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    Jahnke W, Henze C, Winfree A T. Chemical vortex dynamics in three-dimensional excitable media [J].Nature, 1988, (336): 662–665CrossRefGoogle Scholar
  9. [9]
    Nandapurkar P J, Winfree A T. Dynamical stability of untwisted scroll rings in excitable media [J].Phys D, 1989,35: 277–288MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1999

Authors and Affiliations

  • Liu Shenquan
    • 1
  • Lu Qishao
    • 1
  • Huang Kelei
    • 1
  1. 1.Department of Applied Mathematics and PhysicsBeijing University of Aeronautics and AstronauticsBeijingP R China

Personalised recommendations