{"id":153,"date":"2007-10-12T17:07:09","date_gmt":"2007-10-12T17:07:09","guid":{"rendered":"http:\/\/www.complejidadsocial.udd.cl\/?p=153"},"modified":"2007-10-12T17:07:09","modified_gmt":"2007-10-12T17:07:09","slug":"distinguishing-noise-from-chaos","status":"publish","type":"post","link":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/","title":{"rendered":"Distinguishing Noise from Chaos"},"content":{"rendered":"<p>O. A. Rosso, H. A. Larrondo, M. T. Martin, A. Plastino and Miguel Angel Fuentes. Physical Review Letters 99, 154102, doi: 10.1103\/PhysRevLett.99.154102, 2007.<\/p>\n<p><strong>ABSTRACT<\/strong><\/p>\n<p>Chaotic systems share with stochastic processes several properties that make them almost undistinguishable. In this communication we introduce a representation space, to be called the complexity-entropy causality plane. Its horizontal and vertical axis are suitable functionals of the pertinent probability distribution, namely, the entropy of the system and an appropriate statistical complexity measure, respectively. These two functionals are evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the system. Several well-known model-generated time series, usually regarded as being of either stochastic or chaotic nature, are analyzed so as to illustrate the approach. The main achievement of this communication is the possibility of clearly distinguishing between them in our representation space, something that is rather difficult otherwise.<\/p>\n<p><a href=\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/DistinguishingNoisefromChaos.pdf\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-85\" title=\"PDF\" src=\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\" alt=\"\" width=\"40\" height=\"40\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>O. A. Rosso, H. A. Larrondo, M. T. Martin, A. Plastino and Miguel Angel Fuentes. Physical Review Letters 99, 154102, 2007, doi: 10.1103\/PhysRevLett.99.154102.<\/p>\n","protected":false},"author":9192217,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,5],"tags":[],"class_list":["post-153","post","type-post","status-publish","format-standard","hentry","category-papers","category-publications"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Distinguishing Noise from Chaos - Centro de Investigaci\u00f3n en Complejidad Social<\/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:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Distinguishing Noise from Chaos - Centro de Investigaci\u00f3n en Complejidad Social\" \/>\n<meta property=\"og:description\" content=\"O. A. Rosso, H. A. Larrondo, M. T. Martin, A. Plastino and Miguel Angel Fuentes. Physical Review Letters 99, 154102, 2007, doi: 10.1103\/PhysRevLett.99.154102.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/\" \/>\n<meta property=\"og:site_name\" content=\"Centro de Investigaci\u00f3n en Complejidad Social\" \/>\n<meta property=\"article:published_time\" content=\"2007-10-12T17:07:09+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\" \/>\n<meta name=\"author\" content=\"jhc\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"jhc\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/\"},\"author\":{\"name\":\"jhc\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/5b76ef104bf8776a2926aa964b447806\"},\"headline\":\"Distinguishing Noise from Chaos\",\"datePublished\":\"2007-10-12T17:07:09+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/\"},\"wordCount\":151,\"commentCount\":0,\"image\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\",\"articleSection\":[\"PAPERS\",\"PUBLICATIONS\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/\",\"url\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/\",\"name\":\"Distinguishing Noise from Chaos - Centro de Investigaci\u00f3n en Complejidad Social\",\"isPartOf\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\",\"datePublished\":\"2007-10-12T17:07:09+00:00\",\"author\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/5b76ef104bf8776a2926aa964b447806\"},\"breadcrumb\":{\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#primaryimage\",\"url\":\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\",\"contentUrl\":\"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg\",\"width\":40,\"height\":40},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/gobierno.udd.cl\/cics\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distinguishing Noise from Chaos\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#website\",\"url\":\"https:\/\/gobierno.udd.cl\/cics\/\",\"name\":\"Centro de Investigaci\u00f3n en Complejidad Social\",\"description\":\"Facultad de Gobierno - Universidad del Desarrollo\",\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/5b76ef104bf8776a2926aa964b447806\",\"name\":\"jhc\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/d4f227543d44503ecd9209b725c0a5e74781f1e1384cb3c6ef29f0c7536082b0?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/d4f227543d44503ecd9209b725c0a5e74781f1e1384cb3c6ef29f0c7536082b0?s=96&d=mm&r=g\",\"caption\":\"jhc\"},\"url\":\"https:\/\/gobierno.udd.cl\/cics\/author\/jorge-hernandez\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Distinguishing Noise from Chaos - Centro de Investigaci\u00f3n en Complejidad Social","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:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/","og_locale":"en_US","og_type":"article","og_title":"Distinguishing Noise from Chaos - Centro de Investigaci\u00f3n en Complejidad Social","og_description":"O. A. Rosso, H. A. Larrondo, M. T. Martin, A. Plastino and Miguel Angel Fuentes. Physical Review Letters 99, 154102, 2007, doi: 10.1103\/PhysRevLett.99.154102.","og_url":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/","og_site_name":"Centro de Investigaci\u00f3n en Complejidad Social","article_published_time":"2007-10-12T17:07:09+00:00","og_image":[{"url":"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg","type":"","width":"","height":""}],"author":"jhc","twitter_card":"summary_large_image","twitter_misc":{"Written by":"jhc","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#article","isPartOf":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/"},"author":{"name":"jhc","@id":"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/5b76ef104bf8776a2926aa964b447806"},"headline":"Distinguishing Noise from Chaos","datePublished":"2007-10-12T17:07:09+00:00","mainEntityOfPage":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/"},"wordCount":151,"commentCount":0,"image":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#primaryimage"},"thumbnailUrl":"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg","articleSection":["PAPERS","PUBLICATIONS"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/","url":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/","name":"Distinguishing Noise from Chaos - Centro de Investigaci\u00f3n en Complejidad Social","isPartOf":{"@id":"https:\/\/gobierno.udd.cl\/cics\/#website"},"primaryImageOfPage":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#primaryimage"},"image":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#primaryimage"},"thumbnailUrl":"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg","datePublished":"2007-10-12T17:07:09+00:00","author":{"@id":"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/5b76ef104bf8776a2926aa964b447806"},"breadcrumb":{"@id":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#primaryimage","url":"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg","contentUrl":"https:\/\/gobierno.udd.cl\/cics\/files\/2012\/07\/pdf-cics.jpg","width":40,"height":40},{"@type":"BreadcrumbList","@id":"https:\/\/gobierno.udd.cl\/cics\/2007\/10\/12\/distinguishing-noise-from-chaos\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/gobierno.udd.cl\/cics\/"},{"@type":"ListItem","position":2,"name":"Distinguishing Noise from Chaos"}]},{"@type":"WebSite","@id":"https:\/\/gobierno.udd.cl\/cics\/#website","url":"https:\/\/gobierno.udd.cl\/cics\/","name":"Centro de Investigaci\u00f3n en Complejidad Social","description":"Facultad de Gobierno - Universidad del Desarrollo","inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/5b76ef104bf8776a2926aa964b447806","name":"jhc","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/gobierno.udd.cl\/cics\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/d4f227543d44503ecd9209b725c0a5e74781f1e1384cb3c6ef29f0c7536082b0?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d4f227543d44503ecd9209b725c0a5e74781f1e1384cb3c6ef29f0c7536082b0?s=96&d=mm&r=g","caption":"jhc"},"url":"https:\/\/gobierno.udd.cl\/cics\/author\/jorge-hernandez\/"}]}},"featured_image_url":null,"_links":{"self":[{"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/posts\/153","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/users\/9192217"}],"replies":[{"embeddable":true,"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/comments?post=153"}],"version-history":[{"count":0,"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/posts\/153\/revisions"}],"wp:attachment":[{"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/media?parent=153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/categories?post=153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gobierno.udd.cl\/cics\/wp-json\/wp\/v2\/tags?post=153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}