Symmetry-breaking bifurcations in one-dimensional excitable media
- 1 October 1992
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 46 (8) , 5054-5062
- https://doi.org/10.1103/physreva.46.5054
Abstract
A two-species reaction-diffusion model is used to study bifurcations in one-dimensional excitable media. Numerical continuation is used to compute branches of traveling waves and periodic steady states, and linear stability analysis is used to determine bifurcations of these solutions. It is shown that the sequence of symmetry-breaking bifurcations which lead from the homogeneous excitable state to stable traveling waves can be understood in terms of an O(2)-symmetric normal form.Keywords
This publication has 34 references indexed in Scilit:
- The bifurcation structure of waves in excitable chemical systemsThe Journal of Chemical Physics, 1989
- Diffusive Effects on Dispersion in Excitable MediaSIAM Journal on Applied Mathematics, 1989
- Singular perturbation theory of traveling waves in excitable media (a review)Physica D: Nonlinear Phenomena, 1988
- Dispersion of traveling waves in the belousov-zhabotinskii reactionPhysica D: Nonlinear Phenomena, 1988
- Measurement of dispersion relation of chemical waves in an oscillatory reacting mediumThe Journal of Physical Chemistry, 1988
- Sustained chemical waves in an annular gel reactor: a chemical pinwheelNature, 1987
- Geometrical Characteristics Associated with Stability and Bifurcations of Periodic Travelling Waves in Reaction-Diffusion SystemsSIAM Journal on Applied Mathematics, 1985
- Understanding the patterns in the BZ reagentJournal of Statistical Physics, 1985
- The dependence of impulse propagation speed on firing frequency, dispersion, for the Hodgkin-Huxley modelBiophysical Journal, 1981
- Rotating waves as asymptotic solutions of a model chemical reactionThe Journal of Chemical Physics, 1977