{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1361699994092864768.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1063/1.2930766"}},{"identifier":{"@type":"URI","@value":"https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/1.2930766/13857986/037113_1_online.pdf"}}],"dc:title":[{"@value":"Low dimensional behavior of large systems of globally coupled oscillators"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:p>It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1381699994092864769","@type":"Researcher","foaf:name":[{"@value":"Edward Ott"}],"jpcoar:affiliationName":[{"@value":"University of Maryland , College Park, Maryland 20742, USA"}]},{"@id":"https://cir.nii.ac.jp/crid/1381699994092864768","@type":"Researcher","foaf:name":[{"@value":"Thomas M. Antonsen"}],"jpcoar:affiliationName":[{"@value":"University of Maryland , College Park, Maryland 20742, USA"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"10541500"},{"@type":"EISSN","@value":"10897682"}],"prism:publicationName":[{"@value":"Chaos: An Interdisciplinary Journal of Nonlinear Science"}],"dc:publisher":[{"@value":"AIP Publishing"}],"prism:publicationDate":"2008-09-01","prism:volume":"18","prism:number":"3","prism:startingPage":"037113"},"reviewed":"false","url":[{"@id":"https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/1.2930766/13857986/037113_1_online.pdf"}],"createdAt":"2008-09-22","modifiedAt":"2023-07-03","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1050001338017350144","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Phase synchronization between collective rhythms of globally coupled oscillator groups: Noisy identical 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