{"id":33,"date":"2024-03-05T21:42:12","date_gmt":"2024-03-05T21:42:12","guid":{"rendered":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/?p=33"},"modified":"2024-03-05T21:44:01","modified_gmt":"2024-03-05T21:44:01","slug":"tipping-points-and-non-autonom-us-systems","status":"publish","type":"post","link":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/","title":{"rendered":"Tipping points and non-autonomous systems?"},"content":{"rendered":"\n<p>A reason that nonautonomous systems are relevant is that they provide a framework to discuss transitions of a nonlinear system through a &#8220;tipping point&#8221;. For slow variation of an input forcing, nonlinear systems may have sudden changes in the number of stable states due to some of them becoming unstable. This gets even more interesting when there are more rapid chances in input forcing at &#8220;rate dependent&#8221; effects can appear. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>A reason that nonautonomous systems are relevant is that they provide a framework to discuss transitions of a nonlinear system through a &#8220;tipping point&#8221;. For slow variation of an input forcing, nonlinear systems may have sudden changes in the number of stable states due to some of them becoming unstable. This gets even more interesting&hellip; <a class=\"more-link\" href=\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/\">Continue reading <span class=\"screen-reader-text\">Tipping points and non-autonomous systems?<\/span><\/a><\/p>\n","protected":false},"author":1197,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Tipping points and non-autonomous systems? - Applied Nonautonomous Dynamical Systems blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tipping points and non-autonomous systems? - Applied Nonautonomous Dynamical Systems blog\" \/>\n<meta property=\"og:description\" content=\"A reason that nonautonomous systems are relevant is that they provide a framework to discuss transitions of a nonlinear system through a &#8220;tipping point&#8221;. For slow variation of an input forcing, nonlinear systems may have sudden changes in the number of stable states due to some of them becoming unstable. This gets even more interesting&hellip; Continue reading Tipping points and non-autonomous systems?\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/\" \/>\n<meta property=\"og:site_name\" content=\"Applied Nonautonomous Dynamical Systems blog\" \/>\n<meta property=\"article:published_time\" content=\"2024-03-05T21:42:12+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-03-05T21:44:01+00:00\" \/>\n<meta name=\"author\" content=\"pashwin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"pashwin\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/\",\"url\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/\",\"name\":\"Tipping points and non-autonomous systems? - Applied Nonautonomous Dynamical Systems blog\",\"isPartOf\":{\"@id\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/#website\"},\"datePublished\":\"2024-03-05T21:42:12+00:00\",\"dateModified\":\"2024-03-05T21:44:01+00:00\",\"author\":{\"@id\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/#\/schema\/person\/0af5d4c1c8d0228290d3ad6d731e4712\"},\"breadcrumb\":{\"@id\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Tipping points and non-autonomous systems?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/#website\",\"url\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/\",\"name\":\"Applied Nonautonomous Dynamical Systems blog\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/#\/schema\/person\/0af5d4c1c8d0228290d3ad6d731e4712\",\"name\":\"pashwin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/0bb0b8c0309897ea85041e7a2eb4ff65?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/0bb0b8c0309897ea85041e7a2eb4ff65?s=96&d=mm&r=g\",\"caption\":\"pashwin\"},\"url\":\"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/author\/pashwin\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Tipping points and non-autonomous systems? - Applied Nonautonomous Dynamical Systems blog","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/","og_locale":"en_US","og_type":"article","og_title":"Tipping points and non-autonomous systems? - Applied Nonautonomous Dynamical Systems blog","og_description":"A reason that nonautonomous systems are relevant is that they provide a framework to discuss transitions of a nonlinear system through a &#8220;tipping point&#8221;. For slow variation of an input forcing, nonlinear systems may have sudden changes in the number of stable states due to some of them becoming unstable. This gets even more interesting&hellip; Continue reading Tipping points and non-autonomous systems?","og_url":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/","og_site_name":"Applied Nonautonomous Dynamical Systems blog","article_published_time":"2024-03-05T21:42:12+00:00","article_modified_time":"2024-03-05T21:44:01+00:00","author":"pashwin","twitter_card":"summary_large_image","twitter_misc":{"Written by":"pashwin"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/","url":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/","name":"Tipping points and non-autonomous systems? - Applied Nonautonomous Dynamical Systems blog","isPartOf":{"@id":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/#website"},"datePublished":"2024-03-05T21:42:12+00:00","dateModified":"2024-03-05T21:44:01+00:00","author":{"@id":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/#\/schema\/person\/0af5d4c1c8d0228290d3ad6d731e4712"},"breadcrumb":{"@id":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/2024\/03\/05\/tipping-points-and-non-autonom-us-systems\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/"},{"@type":"ListItem","position":2,"name":"Tipping points and non-autonomous systems?"}]},{"@type":"WebSite","@id":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/#website","url":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/","name":"Applied Nonautonomous Dynamical Systems blog","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/#\/schema\/person\/0af5d4c1c8d0228290d3ad6d731e4712","name":"pashwin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/0bb0b8c0309897ea85041e7a2eb4ff65?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/0bb0b8c0309897ea85041e7a2eb4ff65?s=96&d=mm&r=g","caption":"pashwin"},"url":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/author\/pashwin\/"}]}},"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/wp-json\/wp\/v2\/posts\/33"}],"collection":[{"href":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/wp-json\/wp\/v2\/users\/1197"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/wp-json\/wp\/v2\/comments?post=33"}],"version-history":[{"count":2,"href":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/wp-json\/wp\/v2\/posts\/33\/revisions"}],"predecessor-version":[{"id":37,"href":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/wp-json\/wp\/v2\/posts\/33\/revisions\/37"}],"wp:attachment":[{"href":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/wp-json\/wp\/v2\/media?parent=33"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/wp-json\/wp\/v2\/categories?post=33"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.exeter.ac.uk\/appliednonautonomousdynamics\/wp-json\/wp\/v2\/tags?post=33"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}