{"id":26542,"date":"2023-05-01T12:23:37","date_gmt":"2023-05-01T10:23:37","guid":{"rendered":"https:\/\/cio.umh.es\/?p=26542"},"modified":"2024-01-16T12:43:17","modified_gmt":"2024-01-16T11:43:17","slug":"a-review-of-symbolic-dynamics-and-symbolic-reconstruction-of-dynamical-systems","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2023\/05\/01\/a-review-of-symbolic-dynamics-and-symbolic-reconstruction-of-dynamical-systems\/","title":{"rendered":"Yoshito Hirata, &amp; Jos\u00e9 M. Amig\u00f3 (2023). A review of symbolic dynamics and symbolic reconstruction of dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 33."},"content":{"rendered":"<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Yoshito Hirata (Faculty of Engineering, Information and Systems, University of Tsukuba) and Jos\u00e9 Mar\u00eda Amig\u00f3 (Operations Research Center, University Miguel Hern\u00e1ndez of Elche)\u00a0<\/strong><\/p>\n<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Abstract:\u00a0<\/strong><\/p>\n<p>Discretizing a nonlinear time series enables us to calculate its statistics fast and rigorously. Before the turn of the century, the approach using partitions was dominant. In the last two decades, discretization via permutations has been developed to a powerful methodology, while recurrence plots have recently begun to be recognized as a method of discretization. In the meantime, horizontal visibility graphs have also been proposed to discretize time series. In this review, we summarize these methods and compare them from the viewpoint of symbolic dynamics, which is the right framework to study the symbolic representation of nonlinear time series and the inverse process: the symbolic reconstruction of dynamical systems. As we will show, symbolic dynamics is currently a very active research field with interesting applications.<\/p>","protected":false},"excerpt":{"rendered":"<p>Yoshito Hirata (Faculty of Engineering, Information and Systems, University of Tsukuba) and Jos\u00e9 Mar\u00eda Amig\u00f3 (Operations Research Center, University Miguel Hern\u00e1ndez of Elche)\u00a0<br \/>\nAbstract:\u00a0<br \/>\nDiscretizing a nonlinear time series enables us to calculate its statistics fast and rigorously. Before the turn of the century, the approach using partitions was dominant. In the last two decades, discretization via [&#8230;]<\/p>","protected":false},"author":11048,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[369888],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/26542"}],"collection":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/users\/11048"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=26542"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/26542\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=26542"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=26542"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=26542"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}