Fine Structure of Phase Locking

1982/06/28 by Leon Glass, R. Castanedo Pérez · 1 citation
Computer Science · Physics and Astronomy · Mathematics · #Nonlinear Dynamics and Pattern Formation #Chaos control and synchronization #stochastic dynamics and bifurcation #Phase locking #Bistability #Nonlinear system #Simple (philosophy) #Period-doubling bifurcation #Phase (matter) #Physics #Fixed point #CHAOS (operating system) #Statistical physics #Bifurcation #Mathematical analysis #Computer science #Quantum mechanics #Mathematics

paper · doi:10.1103/physrevlett.48.1772

openalex publication_date 1982/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

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.

Citations

• 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 dysrhythmias
• LXXII.The heartbeat considered as a relaxation oscillation, and an electrical model of the heart
• Quantitative universality for a class of nonlinear transformations

Cited by

• Arnold tongue [wikipedia]