The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example - Grantham Research Institute on climate change and the environment<\/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:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example - Grantham Research Institute on climate change and the environment\" \/>\n<meta property=\"og:description\" content=\"In this article, we approach the problem of measuring and interpreting the mid-term climate of a non-autonomous chaotic dynamical system...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\/\" \/>\n<meta property=\"og:site_name\" content=\"Grantham Research Institute on climate change and the environment\" \/>\n<meta property=\"article:modified_time\" content=\"2024-01-29T11:10:15+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/publication\\\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\\\/\",\"url\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/publication\\\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\\\/\",\"name\":\"The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example - Grantham Research Institute on climate change and the environment\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/#website\"},\"datePublished\":\"2023-09-21T07:23:42+00:00\",\"dateModified\":\"2024-01-29T11:10:15+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/publication\\\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\\\/#breadcrumb\"},\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/publication\\\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/publication\\\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Publications\",\"item\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/?post_type=publication\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"All research\",\"item\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/publication-type\\\/new-research\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Research article\",\"item\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/publication-type\\\/research-articles\\\/\"},{\"@type\":\"ListItem\",\"position\":5,\"name\":\"The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/#website\",\"url\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/\",\"name\":\"Grantham Research Institute on climate change and the environment\",\"description\":\"The Grantham Research Institute at LSE carries out world-class research on climate change and the environment.\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/www.lse.ac.uk\\\/granthaminstitute\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-GB\"}]}<\/script>\n","yoast_head_json":{"title":"The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example - Grantham Research Institute on climate change and the environment","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:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\/","og_locale":"en_GB","og_type":"article","og_title":"The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example - Grantham Research Institute on climate change and the environment","og_description":"In this article, we approach the problem of measuring and interpreting the mid-term climate of a non-autonomous chaotic dynamical system...","og_url":"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\/","og_site_name":"Grantham Research Institute on climate change and the environment","article_modified_time":"2024-01-29T11:10:15+00:00","twitter_card":"summary_large_image","twitter_misc":{"Estimated reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\/","url":"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\/","name":"The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example - Grantham Research Institute on climate change and the environment","isPartOf":{"@id":"https:\/\/www.lse.ac.uk\/granthaminstitute\/#website"},"datePublished":"2023-09-21T07:23:42+00:00","dateModified":"2024-01-29T11:10:15+00:00","breadcrumb":{"@id":"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\/#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.lse.ac.uk\/granthaminstitute\/"},{"@type":"ListItem","position":2,"name":"Publications","item":"https:\/\/www.lse.ac.uk\/granthaminstitute\/?post_type=publication"},{"@type":"ListItem","position":3,"name":"All research","item":"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication-type\/new-research\/"},{"@type":"ListItem","position":4,"name":"Research article","item":"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication-type\/research-articles\/"},{"@type":"ListItem","position":5,"name":"The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example"}]},{"@type":"WebSite","@id":"https:\/\/www.lse.ac.uk\/granthaminstitute\/#website","url":"https:\/\/www.lse.ac.uk\/granthaminstitute\/","name":"Grantham Research Institute on climate change and the environment","description":"The Grantham Research Institute at LSE carries out world-class research on climate change and the environment.","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.lse.ac.uk\/granthaminstitute\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-GB"}]}},"taxonomies":{"post_tag":["modelling"],"publication-type":["Research article"]},"_links":{"self":[{"href":"https:\/\/www.lse.ac.uk\/granthaminstitute\/wp-json\/wp\/v2\/publication\/68065","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lse.ac.uk\/granthaminstitute\/wp-json\/wp\/v2\/publication"}],"about":[{"href":"https:\/\/www.lse.ac.uk\/granthaminstitute\/wp-json\/wp\/v2\/types\/publication"}],"author":[{"embeddable":true,"href":"https:\/\/www.lse.ac.uk\/granthaminstitute\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":2,"href":"https:\/\/www.lse.ac.uk\/granthaminstitute\/wp-json\/wp\/v2\/publication\/68065\/revisions"}],"predecessor-version":[{"id":69704,"href":"https:\/\/www.lse.ac.uk\/granthaminstitute\/wp-json\/wp\/v2\/publication\/68065\/revisions\/69704"}],"wp:attachment":[{"href":"https:\/\/www.lse.ac.uk\/granthaminstitute\/wp-json\/wp\/v2\/media?parent=68065"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lse.ac.uk\/granthaminstitute\/wp-json\/wp\/v2\/tags?post=68065"},{"taxonomy":"publication-type","embeddable":true,"href":"https:\/\/www.lse.ac.uk\/granthaminstitute\/wp-json\/wp\/v2\/publication-type?post=68065"},{"taxonomy":"topic_area","embeddable":true,"href":"https:\/\/www.lse.ac.uk\/granthaminstitute\/wp-json\/wp\/v2\/topic_area?post=68065"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":68065,"date":"2023-09-21T08:23:42","date_gmt":"2023-09-21T07:23:42","guid":{"rendered":"https:\/\/www.lse.ac.uk\/granthaminstitute\/?post_type=publication&p=68065"},"modified":"2024-01-29T11:10:15","modified_gmt":"2024-01-29T11:10:15","slug":"the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example","status":"publish","type":"publication","link":"https:\/\/www.lse.ac.uk\/granthaminstitute\/publication\/the-evolution-of-a-non-autonomous-chaotic-system-under-non-periodic-forcing-a-climate-change-example\/","title":{"rendered":"The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example"},"content":{"rendered":"\n

In this article, we approach the problem of measuring and interpreting the mid-term climate of a non-autonomous chaotic dynamical system in the context of climate modeling. To do so, we use a low-dimensional, conceptual model for the Earth system with different timescales of variability and subjected to non-periodic external forcing. We introduce the concepts of an evolution set and its distribution, which are dependent on the starting state of the system, and explore their links to different types of initial condition uncertainty and the rate of external forcing. We define the convergence time as the time that it takes for the evolution distribution of one of the dependent variables to lose memory of its initial condition. We suspect a connection between convergence times and the classical concept of mixing times, but the precise nature of this connection needs to be explored. These results have implications for the design of influential climate and Earth system model ensembles and raise a number of issues of mathematical interest.<\/p>\n\n\n\n

Vir’issimo, F.D., Stainforth, D.A., & Brocker, J. (2023). The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example. Chaos<\/em>.<\/strong><\/p>\n\n\n\n

The Accepted Manuscript is available at the LSERO: https:\/\/eprints.lse.ac.uk\/121591\/