Correspondence between Phase Oscillator Network and Classical XY Model with the Same Infinite-Range Interaction in Statics

• 資料種別: 記事
• タイトル: Correspondence between Phase Oscillator Network and Classical XY Model with the Same Infinite-Range Interaction in Statics
• 著者・編者: Tatsuya Uezu; Tomoyuki Kimoto; Shuji Kiyokawa 他
• 著者標目: Tatsuya Uezu; Tomoyuki Kimoto; Shuji Kiyokawa
• タイトル（掲載誌）: Journal of the Physical Society of Japan
• 巻号年月日等（掲載誌）: 84(3):2015.3
• 掲載巻: 84
• 掲載号: 3
• 掲載ページ: 033001-1-5
• 掲載年月日（W3CDTF）: 2015-03
• ISSN（掲載誌）: 0031-9015
• ISSN-L（掲載誌）: 0031-9015
• 出版事項（掲載誌）: Tokyo : Physical Society of Japan
• 出版地（国名コード）: JP
• 本文の言語コード: eng
• NDLC: ZM35
• 対象利用者: 一般
• 所蔵機関: 国立国会図書館
• 請求記号: Z53-A404
• 連携機関・データベース: 国立国会図書館 : 国立国会図書館雑誌記事索引; https://ndlsearch.ndl.go.jp
• 書誌ID（NDLBibID）: 026247828; http://id.ndl.go.jp/bib/026247828
• 整理区分コード: 632

• 要約等: We study phase oscillator networks with distributed natural frequencies and classical XY models, both of which have a class of infinite-range interactions in common. We find that the integral kernel of the self-consistent equations (SCEs) for oscillator networks corresponds to that of the saddle point equations (SPEs) for XY models, and that the quenched randomness (distributed natural frequencies) corresponds to thermal noise. We find a sufficient condition under which the probability density of natural frequency distributions is one-humped, so that the kernel in an oscillator network is strictly decreasing, as in the XY model. Furthermore, taking the uniform and Mexican-hat-type interactions, we prove the one-to-one correspondence between the solutions of the SCEs and SPEs. As an application of the correspondence, we study the associative-memory-type interaction. In the XY model with this interaction, there exists a peculiar one-parameter family of solutions. For the oscillator network, we find a nontrivial solution, i.e., a limit cycle oscillation.; 本論文の著作権は一般社団法人日本物理学会(The Physical Society of Japan)が保有しています。
• DOI: 10.7566/jpsj.84.033001; https://doi.org/10.7566/jpsj.84.033001; 10.48550/arxiv.1412.7850; https://doi.org/10.48550/arxiv.1412.7850
• オンライン閲覧公開範囲: インターネット公開
• 関連情報（URI）: http://hdl.handle.net/10935/3918; https://nara-wu.repo.nii.ac.jp/records/2002213; http://id.ndl.go.jp/bib/026247828; https://ndlsearch.ndl.go.jp/books/R000000004-I026247828; https://journals.jps.jp/doi/pdf/10.7566/JPSJ.84.033001
• 参照: Correspondence between phase oscillator network and classical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math> model with the same random and frustrated interactions; https://cir.nii.ac.jp/crid/1050564288847321856
• 参照: Analysis of XY model with mexican-hat interaction on a circle : Derivation of saddle point equations and study of bifurcation structure; https://cir.nii.ac.jp/crid/1050282813367803008; Continuous Attractor that Appears in Autoassociative Memory Model Extended to XY Spin System; https://cir.nii.ac.jp/crid/1050282813368581632; Solvable Model of a Phase Oscillator Network on a Circle with Infinite-Range Mexican-Hat-Type Interaction; https://cir.nii.ac.jp/crid/1050564288345248768; Analysis of a solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction; https://cir.nii.ac.jp/crid/1050845763322002816; Center manifold reduction for large populations of globally coupled phase oscillators; https://cir.nii.ac.jp/crid/1050861482657920000; Exact results for the Kuramoto model with a bimodal frequency distribution; https://cir.nii.ac.jp/crid/1360011144093720960; Long time evolution of phase oscillator systems; https://cir.nii.ac.jp/crid/1360855568928791808; Low dimensional behavior of large systems of globally coupled oscillators; https://cir.nii.ac.jp/crid/1361699994092864768; Mean field and cavity analysis for coupled oscillator networks; https://cir.nii.ac.jp/crid/1361699994865731584; The Kuramoto model: A simple paradigm for synchronization phenomena; https://cir.nii.ac.jp/crid/1361699995623526400; Quantum Field Theory and Critical Phenomena; https://cir.nii.ac.jp/crid/1361981469151684992; Existence of hysteresis in the Kuramoto model with bimodal frequency distributions; https://cir.nii.ac.jp/crid/1362825894860647808; The Spectrum of the Partially Locked State for the Kuramoto Model; https://cir.nii.ac.jp/crid/1363670319546566016; Chemical Oscillations, Waves, and Turbulence; https://cir.nii.ac.jp/crid/1363670321219846272; Biological rhythms and the behavior of populations of coupled oscillators; https://cir.nii.ac.jp/crid/1363951795881402112; Dynamical Behavior of Phase Oscillator Networks on the Bethe Lattice; https://cir.nii.ac.jp/crid/1390282679173476480; Analysis of XY model with mexican-hat interaction on a circle; https://cir.nii.ac.jp/crid/1520573330710638720
• 連携機関・データベース: 国立情報学研究所 : CiNii Research; https://cir.nii.ac.jp/
• 提供元機関・データベース: 学術機関リポジトリデータベース; https://irdb.nii.ac.jp; 雑誌記事索引データベース; https://ndlsearch.ndl.go.jp; Crossref; https://www.crossref.org; CiNii Articles
• 書誌ID（NDLBibID）: 026247828; http://id.ndl.go.jp/bib/026247828
• NII論文ID: 120006657923