Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators
Physical Review LettersPublished 7 May 2001Open access
Joel T. Ariaratnam, Steven H. Strogatz
Citations146
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TL;DR
The first bifurcation analysis of the Winfree mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators is given, for a tractable special case.
Abstract
In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.
Keywords
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