Fine Structure of Phase Locking
- 28 June 1982
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 48 (26), 1772-1775
- https://doi.org/10.1103/PhysRevLett.48.1772
Abstract
A simple mathematical model is given which shows how phase locking, bistability, period-doubling bifurcations, and chaos may result from periodic stimulation of nonlinear oscillators. A new fixed-point theorem, which extends the classic results of Arnold, is used in the analysis.Keywords
This publication has 16 references indexed in Scilit:
- Evidence for Universal Chaotic Behavior of a Driven Nonlinear OscillatorPhysical Review Letters, 1982
- Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmiasJournal of Mathematical Biology, 1982
- Phase Locking, Period-Doubling Bifurcations, and Irregular Dynamics in Periodically Stimulated Cardiac CellsScience, 1981
- Period Doubling and Chaotic Behavior in a Driven Anharmonic OscillatorPhysical Review Letters, 1981
- Transition to turbulence for doubly periodic flowsPhysics Letters A, 1980
- Chaotic response of a limit cycleJournal of Statistical Physics, 1979
- The simplest case of a strange attractorPhysics Letters A, 1978
- Quantitative universality for a class of nonlinear transformationsJournal of Statistical Physics, 1978
- A Second Order Differential Equation with Singular SolutionsAnnals of Mathematics, 1949
- On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1-y 2 )y˙ + y = b λk cos(λl + α), k LargeJournal of the London Mathematical Society, 1945