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Title: Emergent behaviors of a holonomic particle system on a sphere

We study sufficient conditions for the asymptotic emergence of synchronous behaviors in a holonomic particle system on a sphere, which was recently introduced by Lohe [“Non-Abelian Kuramoto model and synchronization,” J. Phys. A: Math. Theor. 42, 395101–395126 (2009)]. These conditions depend only on the coupling strength and initial position diameter. For identical particles, we show that the position diameter approaches zero asymptotically under these sufficient conditions, i.e., all particles approach to the same position. For non-identical particles, the particle positions do not shrink to one point, but can be squeezed into some small region whose diameter is inversely proportional to the coupling strength, when the coupling strength is large. We also provide several numerical results to confirm our analytical findings.
Authors:
;  [1] ;  [2]
  1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747 (Korea, Republic of)
  2. Department of Mathematical Science, KAIST, Daejeon 305-701 (Korea, Republic of)
Publication Date:
OSTI Identifier:
22250599
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 5; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; COUPLING; SPHERES; SYNCHRONIZATION