Structure of complex-periodic and chaotic media with spiral waves
- 1 November 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 54 (5) , 5469-5481
- https://doi.org/10.1103/physreve.54.5469
Abstract
The spatiotemporal structure of reactive media supporting a solitary spiral wave is studied for systems where the local reaction law exhibits a period-doubling cascade to chaos. This structure is considerably more complex than that of simple period-1 oscillatory media. As one moves from the core of the spiral wave the local dynamics takes the form of perturbed, period-doubled orbits whose character varies with spatial location relative to the core. An important feature of these media is the existence of a curve where the local dynamics is effectively period-1. This curve arises as a consequence of the necessity to reconcile the conflict between the global topological organization of the medium induced by the presence of a spiral wave and the topological phase space structure of local orbits determined by the reaction rate law. Due to their general topological nature, the phenomena described here should be observable in a broad class of systems with complex-periodic behavior. © 1996 The American Physical Society.Keywords
All Related Versions
This publication has 13 references indexed in Scilit:
- Phase Synchronization of Chaotic OscillatorsPhysical Review Letters, 1996
- Spiral Waves in Chaotic SystemsPhysical Review Letters, 1996
- Long-range order with local chaos in lattices of diffusively coupled ODEsPhysica D: Nonlinear Phenomena, 1994
- Effects of molecular fluctuations on chemical oscillations and chaosThe Journal of Chemical Physics, 1994
- Varieties of spiral wave behavior: An experimentalist’s approach to the theory of excitable mediaChaos: An Interdisciplinary Journal of Nonlinear Science, 1991
- Complex periodic oscillations and Farey arithmetic in the Belousov–Zhabotinskii reactionThe Journal of Chemical Physics, 1986
- Chemical Oscillations, Waves, and TurbulencePublished by Springer Nature ,1984
- Irregular Oscillations in a Realistic Abstract Quadratic Mass Action SystemZeitschrift für Naturforschung A, 1980
- The Geometry of Biological TimePublished by Springer Nature ,1980
- The topological theory of defects in ordered mediaReviews of Modern Physics, 1979