{"id":13631,"date":"2026-04-24T13:16:23","date_gmt":"2026-04-24T17:16:23","guid":{"rendered":"https:\/\/blogs.mathworks.com\/cleve\/?p=13631"},"modified":"2026-04-24T13:16:23","modified_gmt":"2026-04-24T17:16:23","slug":"kuramoto-oscillators","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/cleve\/2026\/04\/24\/kuramoto-oscillators\/","title":{"rendered":"Kuramoto Oscillators"},"content":{"rendered":"<div class=\"content\">\r\n<h3>Kuramoto Oscillators<\/h3>\r\n<p>I have blogged before about the work Indika Rajapakse, Steve Smale and I are doing to investigate the stability of Kuramoto oscillators.<\/p>\r\n<p>\r\n<a href=\"https:\/\/blogs.mathworks.com\/cleve\/2020\/07\/08\/a-mesmerizing-animation\/\">https:\/\/blogs.mathworks.com\/cleve\/2020\/07\/08\/a-mesmerizing-animation\/<\/a>\r\n<\/p>\r\n<p>\r\n<a href=\"https:\/\/blogs.mathworks.com\/cleve\/2019\/10\/30\/stability-of-kuramoto-oscillators\/\">https:\/\/blogs.mathworks.com\/cleve\/2019\/10\/30\/stability-of-kuramoto-oscillators\/<\/a>\r\n<\/p>\r\n<p>\r\n<a href=\"https:\/\/blogs.mathworks.com\/cleve\/2019\/09\/16\/experiments-with-kuramoto-oscillators\/\">https:\/\/blogs.mathworks.com\/cleve\/2019\/09\/16\/experiments-with-kuramoto-oscillators\/<\/a>\r\n<\/p>\r\n<p>\r\n<img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/cleve\/files\/mesmerizer_5.gif\" alt=\"\"> <\/p>\r\n<p>Here is a link to the latest version of our paper.<\/p>\r\n<p>\r\n<a href=\"https:\/\/blogs.mathworks.com\/cleve\/files\/Kuramoto.pdf\">https:\/\/blogs.mathworks.com\/cleve\/files\/Kuramoto.pdf<\/a>\r\n<\/p>\r\n<script language=\"JavaScript\"> <!-- \r\n    function grabCode_a3fc9843d7d748449b7723c6d2f18e48() {\r\n        \/\/ Remember the title so we can use it in the new page\r\n        title = document.title;\r\n\r\n        \/\/ Break up these strings so that their presence\r\n        \/\/ in the Javascript doesn't mess up the search for\r\n        \/\/ the MATLAB code.\r\n        t1='a3fc9843d7d748449b7723c6d2f18e48 ' + '##### ' + 'SOURCE BEGIN' + ' #####';\r\n        t2='##### ' + 'SOURCE END' + ' #####' + ' a3fc9843d7d748449b7723c6d2f18e48';\r\n    \r\n        b=document.getElementsByTagName('body')[0];\r\n        i1=b.innerHTML.indexOf(t1)+t1.length;\r\n        i2=b.innerHTML.indexOf(t2);\r\n \r\n        code_string = b.innerHTML.substring(i1, i2);\r\n        code_string = code_string.replace(\/REPLACE_WITH_DASH_DASH\/g,'--');\r\n\r\n        \/\/ Use \/x3C\/g instead of the less-than character to avoid errors \r\n        \/\/ in the XML parser.\r\n        \/\/ Use '\\x26#60;' instead of '<' so that the XML parser\r\n        \/\/ doesn't go ahead and substitute the less-than character. \r\n        code_string = code_string.replace(\/\\x3C\/g, '\\x26#60;');\r\n\r\n        copyright = 'Copyright 2026 The MathWorks, Inc.';\r\n\r\n        w = window.open();\r\n        d = w.document;\r\n        d.write('<pre>\\n');\r\n        d.write(code_string);\r\n\r\n        \/\/ Add copyright line at the bottom if specified.\r\n        if (copyright.length > 0) {\r\n            d.writeln('');\r\n            d.writeln('%%');\r\n            if (copyright.length > 0) {\r\n                d.writeln('% _' + copyright + '_');\r\n            }\r\n        }\r\n\r\n        d.write('<\/pre>\\n');\r\n\r\n        d.title = title + ' (MATLAB code)';\r\n        d.close();\r\n    }   \r\n     --> <\/script>\r\n<p style=\"text-align: right; font-size: xx-small; font-weight:lighter;   font-style: italic; color: gray\">\r\n<br>\r\n<a href=\"javascript:grabCode_a3fc9843d7d748449b7723c6d2f18e48()\"><span style=\"font-size: x-small;        font-style: italic;\">Get \r\n      the MATLAB code <noscript>(requires JavaScript)<\/noscript>\r\n<\/span><\/a>\r\n<br>\r\n<br>\r\n      Published with MATLAB&reg; R2024b<br>\r\n<\/p>\r\n<\/div>\r\n<!--\r\na3fc9843d7d748449b7723c6d2f18e48 ##### SOURCE BEGIN #####\r\n%% Kuramoto Oscillators\r\n% I have blogged before about the work\r\n% Indika Rajapakse, Steve Smale and I are doing to investigate\r\n% the stability of Kuramoto oscillators.\r\n%\r\n% <https:\/\/blogs.mathworks.com\/cleve\/2020\/07\/08\/a-mesmerizing-animation\/>\r\n%\r\n% <https:\/\/blogs.mathworks.com\/cleve\/2019\/10\/30\/stability-of-kuramoto-oscillators\/>\r\n%\r\n% <https:\/\/blogs.mathworks.com\/cleve\/2019\/09\/16\/experiments-with-kuramoto-oscillators\/>\r\n%\r\n% <<mesmerizer_5.gif>>\r\n%\r\n% Here is a link to the latest version of our paper.\r\n%\r\n% <https:\/\/blogs.mathworks.com\/cleve\/files\/Kuramoto.pdf>\r\n##### SOURCE END ##### a3fc9843d7d748449b7723c6d2f18e48\r\n-->\r\n","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img decoding=\"async\"  class=\"img-responsive\" src=\"https:\/\/blogs.mathworks.com\/cleve\/files\/mesmerizer_5.gif\" onError=\"this.style.display ='none';\" \/><\/div><p>\r\nKuramoto Oscillators\r\nI have blogged before about the work Indika Rajapakse, Steve Smale and I are doing to investigate the stability of Kuramoto... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/cleve\/2026\/04\/24\/kuramoto-oscillators\/\">read more >><\/a><\/p>","protected":false},"author":78,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[24,23,60,16],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/13631"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/users\/78"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/comments?post=13631"}],"version-history":[{"count":3,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/13631\/revisions"}],"predecessor-version":[{"id":13637,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/13631\/revisions\/13637"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media?parent=13631"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/categories?post=13631"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/tags?post=13631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}