2000/12/31 by Hiroshi Kori, Yoshiki Kuramoto · 3 citations
Computer Science · Neuroscience · Physics and Astronomy · #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #cond-mat.dis-nn #nlin.AO #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.63.046214
10 pages, 14 figures, RevTex, twocolumn, to appear in Phys. Rev. E
arxiv created 2001/01/12 · openalex publication_date 2001/03/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.