Scroll waves in isotropic excitable media: Linear instabilities, bifurcations, and restabilized states
- 11 April 2002
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 65 (4), 046235
- https://doi.org/10.1103/physreve.65.046235
Abstract
Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are seen to be unstable in different regions of parameter space. The corresponding bifurcations and bifurcated states are characterized by performing direct numerical simulations. In addition, computations of the adjoint linear stability operator eigenmodes are also performed and serve to obtain a number of matrix elements characterizing the long-wavelength deformations of scroll waves. DOI: http://dx.doi.org/10.1103/PhysRevE.65.046235 © 2002 The American Physical SocietyKeywords
This publication has 39 references indexed in Scilit:
- Diffusion-Induced Vortex Filament Instability in 3-Dimensional Excitable MediaPhysical Review Letters, 1999
- Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systemsPhysical Review E, 1998
- Quantitative optical tomography of chemical waves and their organizing centersChaos: An Interdisciplinary Journal of Nonlinear Science, 1996
- Destabilization of Three-Dimensional Rotating Chemical Waves in an Inhomogeneous BZ ReactionThe Journal of Physical Chemistry, 1996
- Electrical Turbulence in Three-Dimensional Heart MuscleScience, 1994
- Tension of organizing filaments of scroll wavesPhilosophical Transactions A, 1994
- Varieties of spiral wave behavior: An experimentalist’s approach to the theory of excitable mediaChaos: An Interdisciplinary Journal of Nonlinear Science, 1991
- Helical organizing centers in excitable mediaCanadian Journal of Physics, 1990
- Three-dimensional twisted vortices in an excitable chemical mediumNature, 1990
- Two regimes of the scroll ring drift in the three-dimensional active mediaPhysica D: Nonlinear Phenomena, 1987