Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators

Authors :: Steven H. Strogatz
Joel T. Ariaratnam
Publication Year :: 2001
Publisher :: The American Physical Society, 2001.
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 novel hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.<br />Comment: 4 pages, 4 figures