Member access

4-Traders Homepage  >  News

News

Latest NewsCompaniesMarketsEconomy & ForexCommoditiesHot NewsMost Read NewsRecomm.Business LeadersVideosCalendar 
The feature you requested does not exist. However, we suggest the following feature:

New Findings on Dynamic Systems from Kyushu University Summarized (A proof of the Kuramoto conjecture for a bifurcation structure of the...

05/27/2015 | 05:57pm US/Eastern

New Findings on Dynamic Systems from Kyushu University Summarized (A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model)

By a News Reporter-Staff News Editor at Journal of Mathematics -- Investigators publish new report on Dynamic Systems. According to news reporting originating in Fukuoka, Japan, by VerticalNews editors, the research stated, "The Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as coupled phase oscillators. In this paper, a bifurcation structure of the infinite-dimensional Kuramoto model is investigated."

The news reporters obtained a quote from the research from Kyushu University, "A purpose here is to prove the bifurcation diagram of the model conjectured by Kuramoto in 1984; if the coupling strength K between oscillators, which is a parameter of the system, is smaller than some threshold K-C, the de-synchronous state (trivial steady state) is asymptotically stable, while if K exceeds K-C, a non-trivial stable solution, which corresponds to the synchronization, bifurcates from the de-synchronous state. One of the difficulties in proving the conjecture is that a certain non-selfadjoint linear operator, which defines a linear part of the Kuramoto model, has the continuous spectrum on the imaginary axis. Hence, the standard spectral theory is not applicable to prove a bifurcation as well as the asymptotic stability of the steady state. In this paper, the spectral theory on a space of generalized functions is developed with the aid of a rigged Hilbert space to avoid the continuous spectrum on the imaginary axis. Although the linear operator has an unbounded continuous spectrum on a Hilbert space, it is shown that it admits a spectral decomposition consisting of a countable number of eigenfunctions on a space of generalized functions. The semigroup generated by the linear operator will be estimated with the aid of the spectral theory on a rigged Hilbert space to prove the linear stability of the steady state of the system. The center manifold theory is also developed on a space of generalized functions. It is proved that there exists a finite-dimensional center manifold on a space of generalized functions, while a center manifold on a Hilbert space is of infinite dimension because of the continuous spectrum on the imaginary axis."

According to the news reporters, the research concluded: "These results are applied to the stability and bifurcation theory of the Kuramoto model to obtain a bifurcation diagram conjectured by Kuramoto."

For more information on this research see: A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model. Ergodic Theory and Dynamical Systems, 2015;35():762-834. Ergodic Theory and Dynamical Systems can be contacted at: Cambridge Univ Press, 32 Avenue Of The Americas, New York, NY 10013-2473, USA. (Cambridge University Press - www.cambridge.org; Ergodic Theory and Dynamical Systems - journals.cambridge.org/action/displayJournal?jid=ETS)

Our news correspondents report that additional information may be obtained by contacting H. Chiba, Kyushu University, Inst Math, Fukuoka 8190395, Japan.

Keywords for this news article include: Asia, Japan, Fukuoka, Dynamic Systems

Our reports deliver fact-based news of research and discoveries from around the world. Copyright 2015, NewsRx LLC

(c) 2015 NewsRx LLC, source Science Newsletters

React to this article
Latest news
Date Title
05:57p BUSINESS MACHINES : Patent Application Titled "Latch Mechanism for Securing an Electronic Module" Published Online
05:57p Firestone Reminds Truck Owners of Their Truck's Full Potential and the Workmanship That Keeps It Running
05:57p Researchers Submit Patent Application, "Double Cut Single Point Cutoff Tool for Cutting and Finishing an End Surface of a Fuel Injector Pole Piece",...
05:57p New Findings on Dynamic Systems from Kyushu University Summarized (A proof of the Kuramoto conjecture for a bifurcation structure of the...
05:56p Study Results from University of Science Malaysia in the Area of Bioenergy Reported [Effects of process parameters of various pretreatments on...
05:56p KONE : Researchers Submit Patent Application, "Brake", for Approval
05:56p IOU FINANCIAL : Results for the Three Month Period Ended March 31, 2015
05:56p DTS Reports Inducement Grants Under Nasdaq Listing Rule 56354
05:56p NICHIAS : Patent Issued for Heat Retention Member for Cylinder Bore Wall, Internal Combustion Engine, and Automobile
05:55p Trademark Application for "DRAX" Filed by Walt Disney Company Limited
Latest news
Advertisement
Hot News 
MTY NV : Netherlands stocks higher at close of trade; AEX up 1.44%
SYNERGY HEALTHCARE : Form 8.5 (EPT/RI) - Synergy Health plc
MICHAEL KORS : Announces Fourth Quarter and Annual Fiscal 2015 Results
MERU NETWORKS : Fortinet Announces Agreement to Acquire Meru Networks
DJI : Price Monitoring Extension
Most Read News
02:10a PLUS500 : AGM Trading Update and Statement
05/26DJSINGAPORE AIRLINES : Flight to Shanghai on Saturday Temporarily Lost Engine Power, Landed Safely
02:08p Tiffany's sales, profit beat on higher tourist spending in Europe
05/26DJGRAIN HIGHLIGHTS : Top Stories Of The Day
05/26 CTBC FINANCIAL : bank will acquire of 100% stake in CITIC Bank International (China) Limited for HK$ equivalent of CNY 2.353 billion in cash.
Most recommended articles
05:55pDJTeva Reports Small Stake in Mylan
05:48pDJTransocean Hires Mark May as CFO
05:46pDJOil Prices Fall, Taking Cues From Dollar
05:35pDJGerman Finance Minister Urges G-7 to Seek Resolutions
05:29p Greece, creditors have converged in talks but still room to cover - minister