Colliding Waves in a Model Excitable Medium: Preservation, Annihilation, and Bifurcation
- 13 October 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 79 (15) , 2803-2806
- https://doi.org/10.1103/physrevlett.79.2803
Abstract
We analyze the transition from annihilation to preservation of colliding waves. The analysis exploits the similarity between the local and global phase portraits of the system. The transition is shown to be the infinite-dimensional analog of the creation and annihilation of limit cycles in the plane via a homoclinic Andronov bifurcation, and has parallels to the nucleation theory of first-order phase transitions.Keywords
This publication has 11 references indexed in Scilit:
- Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion systemPhilosophical Transactions A, 1994
- Solitons in a surface reactionPhysical Review Letters, 1991
- Kink-antikink dissociation and annihilation: A collective-coordinate descriptionPhysical Review A, 1987
- A model for pattern formation on the shells of molluscsJournal of Theoretical Biology, 1987
- Chemical Oscillations, Waves, and TurbulencePublished by Springer Nature ,1984
- Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector FieldsPublished by Springer Nature ,1983
- Intermittent transition to turbulence in dissipative dynamical systemsCommunications in Mathematical Physics, 1980
- On the existence of hysteresis in a transition to chaos after a single bifurcationJournal de Physique Lettres, 1980
- Dynamics of the Josephson junctionQuarterly of Applied Mathematics, 1978
- A quantitative description of membrane current and its application to conduction and excitation in nerveThe Journal of Physiology, 1952