2024-03-29T05:10:40Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/172072022-11-17T02:08:08Zhdl_2115_20057hdl_2115_148Slow switching in globally coupled oscillators: robustness and occurrence through delayed couplingKori, HiroshiKuramoto, Yoshiki424The 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.American Physical SocietyJournal Articleapplication/pdfhttp://hdl.handle.net/2115/17207https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/17207/1/PRE63-046214.pdf1063-651X1095-3787Physical Review E6340462142001-03-29enginfo:doi/10.1103/PhysRevE.63.046214Copyright © 2001 American Physical Societypublisher