Nonchaotic Transition from Quasiperiodicity to Complete Phase Locking
- 10 October 1988
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 61 (15) , 1679-1682
- https://doi.org/10.1103/physrevlett.61.1679
Abstract
We show the existence of a generic integrate-and-fire phenomenon which separates the transition to complete phase locking from the transition to chaos. We argue that our picture provides a natural explanation of "missing" hysteretic bands in the Belousov-Zhabotinskii reaction. In addition, we explain the origin of experimentally observed "deviations from universality" and bumps in the Arnold tongues in driven relaxation oscillators.Keywords
This publication has 14 references indexed in Scilit:
- Deviations from universality in the transition from quasiperiodicity to chaosPhysical Review Letters, 1987
- Complex periodic oscillations and Farey arithmetic in the Belousov–Zhabotinskii reactionThe Journal of Chemical Physics, 1986
- Fractal structure of the complete devil’s staircase in dissipative systems described by a driven damped-pendulum equation with a distorted potentialPhysical Review B, 1985
- Josephson junction at the onset of chaos: A complete devil’s staircasePhysical Review B, 1985
- Transition to chaos by interaction of resonances in dissipative systems. I. Circle mapsPhysical Review A, 1984
- Systematic design of chemical oscillators. 17. Birhythmicity and compound oscillation in coupled chemical oscillators: chlorite-bromate-iodide systemJournal of the American Chemical Society, 1983
- Integrate-and-Fire Models of Nerve Membrane Response to Oscillatory InputSIAM Journal on Applied Mathematics, 1981
- A simple model for phase locking of biological oscillatorsJournal of Mathematical Biology, 1979
- A model for phasic and tonic repetitively firing neuronal encodersBiological Cybernetics, 1973
- Studies with artificial neurons, I: properties and functions of an artificial neuronBiological Cybernetics, 1961