Contractivity of Transport Distances for the Kinetic Kuramoto Equation

Cited 25 time in webofscience Cited 0 time in scopus
  • Hit : 36
  • Download : 0
We present synchronization and contractivity estimates for the kinetic Kuramoto model obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto oscillators, we present an admissible class of initial data leading to time-asymptotic complete synchronization, that is, all measure valued solutions converge to the traveling Dirac measure concentrated on the initial averaged phase. In the case of non-identical oscillators, we show that the velocity field converges to the average natural frequency proving that the oscillators move asymptotically with the same frequency under suitable assumptions on the initial configuration. If two initial Radon measures have the same natural frequency density function and strength of coupling, we show that the Wasserstein -distance between corresponding measure valued solutions is exponentially decreasing in time. This contraction principle is more general than previous -contraction properties of the Kuramoto phase model.
Publisher
SPRINGER
Issue Date
2014-07
Language
English
Article Type
Article
Citation

JOURNAL OF STATISTICAL PHYSICS, v.156, no.2, pp.395 - 415

ISSN
0022-4715
DOI
10.1007/s10955-014-1005-z
URI
http://hdl.handle.net/10203/278733
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 25 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0