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Chaos : Stability diagram for the forced Kuramoto model

By Lauren M. Childs and Steven H. Strogatz

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Book Id: WPLBN0002169309
Format Type: PDF eBook :
File Size: Serial Publication
Reproduction Date: 31 December 2008

Title: Chaos : Stability diagram for the forced Kuramoto model  
Author: Lauren M. Childs and Steven H. Strogatz
Volume: Issue : December 2008
Language: English
Subject: Science, Physics, Natural Science
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Chaos Collection
Historic
Publication Date:
Publisher: American Institute of Physics

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Childs And Steven H. Strogat, L. M. (n.d.). Chaos : Stability diagram for the forced Kuramoto model. Retrieved from http://hawaiilibrary.net/


Description
Description: We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry, and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while also trying to lock onto an external drive. Previous work on the forced Kuramoto model uncovered two main types of attractors, called forced entrainment and mutual entrainment, but the details of the bifurcations between them were unclear. Here we present a complete bifurcation analysis of the model for a special case in which the infinite-dimensional dynamics collapse to a two-dimensional system. Exact results are obtained for the locations of Hopf, saddle-node, and Takens–Bogdanov bifurcations. The resulting stability diagram bears a striking resemblance to that for the weakly nonlinear forced van der Pol oscillator.

 

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