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Slow switching in globally coupled oscillators: robustness and occurrence through delayed coupling

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Title: Slow switching in globally coupled oscillators: robustness and occurrence through delayed coupling
Authors: Kori, Hiroshi Browse this author
Kuramoto, Yoshiki Browse this author
Issue Date: 29-Mar-2001
Publisher: American Physical Society
Journal Title: Physical Review E
Volume: 63
Issue: 4
Start Page: 046214
Publisher DOI: 10.1103/PhysRevE.63.046214
Abstract: The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the formation of a heteroclinic loop connecting a pair of clustered states of the population. We argue that the same behavior can arise in a wider class of oscillator models with the amplitude degree of freedom. We also argue how such heteroclinic loops arise inevitably and persist robustly in a homogeneous population of globally coupled oscillators. Although a heteroclinic loop might seem to arise only exceptionally, we find that it appears rather easily by introducing time delay into a population which would otherwise exhibit perfect phase synchrony. We argue that the appearance of the heteroclinic loop induced by the delayed coupling is then characterized by transcritical and saddle-node bifurcations. Slow switching arises when a system with a heteroclinic loop is weakly perturbed. This will be demonstrated with a vector model by applying weak noises. Other types of weak symmetry-breaking perturbations can also cause slow switching. ©2001 The American Physical Society.
Rights: Copyright © 2001 American Physical Society
Relation: http://www.aps.org/
Type: article
URI: http://hdl.handle.net/2115/17207
Appears in Collections:電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 郡 宏

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