{"id":361,"date":"2012-06-07T02:27:57","date_gmt":"2012-06-07T08:27:57","guid":{"rendered":"http:\/\/www.comm.utoronto.ca\/dkundur\/?page_id=361"},"modified":"2012-08-22T02:28:00","modified_gmt":"2012-08-22T08:28:00","slug":"dynamical-systems","status":"publish","type":"page","link":"https:\/\/www.comm.utoronto.ca\/dkundur\/research\/dynamical-systems\/","title":{"rendered":"Dynamical Systems"},"content":{"rendered":"<table class=\"alignright\" width=\"250\" border=\"0\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td>\n<h4>Other Research Areas<\/h4>\n<p><a style=\"display:none;\" id=\"ddetlink974762816\" href=\"javascript:expand(document.getElementById('ddet974762816'))\">Expand List<\/a>\n<div class=\"ddet_div\" id=\"ddet974762816\"><script language=\"JavaScript\" type=\"text\/javascript\">expand(document.getElementById('ddet974762816'));expand(document.getElementById('ddetlink974762816'))<\/script><\/p>\n<ul>\n<li><a href=\"\/dkundur\/smart-grid\">Smart Grid<\/a><\/li>\n<li><a href=\"\/dkundur\/cyber-physical-systems\/\">Cyber-Physical Systems<\/a><\/li>\n<li><a href=\"\/dkundur\/multimedia-and-sensor-networks\/\">Multimedia &amp; Sensor Networks<\/a><\/li>\n<li><a href=\"\/dkundur\/dynamical-systems\/\">Dynamical Systems<\/a><\/li>\n<li><a href=\"\/dkundur\/digital-forensics\/\">Digital Forensics<\/a><\/li>\n<li><a href=\"\/dkundur\/physical-layer-security\/\">Physical Layer Security<\/a><\/li>\n<li><a href=\"\/dkundur\/multimedia-security-and-drm\/\">Multimedia Security<\/a><\/li>\n<li><a href=\"\/dkundur\/blind-image-restoration\/\">Blind Image Restoration<\/a><\/li>\n<li><a href=\"\/dkundur\/image-fusion\/\">Image Fusion<\/a><\/li>\n<\/ul>\n<p><\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Application of Dynamical Systems<\/h1>\n<p style=\"text-align: left;\"><img decoding=\"async\" class=\"lazyload attachment-80x60 alignleft\" title=\"Dynamical Systems\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27200%27%20height%3D%27200%27%20viewBox%3D%270%200%20200%20200%27%3E%3Crect%20width%3D%27200%27%20height%3D%27200%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"\/dkundur\/wp-content\/uploads\/DynamicalSystems.png\" alt=\"Dynamical Systems\" width=\"200\" height=\"200\" \/><\/p>\n<p>Dynamical systems describe the time-evolution of a state vector. The state vector characterizes (usually completely) the posture, status or mode of a given system. Dynamical systems in contrast to algebraic systems account for the time-evolution and transient conditions within a system. Thus the dynamics of a given system are considered to have died out when at state-state.<\/p>\n<p>Dynamical\u00a0systems are typically described by ordinary differential equations (continuous-time) or ordinary difference equations (discrete-time). Visually, the behavior of a dynamical system is shown as motion of a state vector in an appropriate state-space. Nonlinear dynamical systems allow for rich behavior that can be employed for lightweight modeling of a variety of systems. Our research focuses on harnessing such systems for modeling (e.g.,<a href=\"\/dkundur\/smart-grid\/\"> smart grid<\/a> systems) and robotic systems.<\/p>\n<h5>Related Publications<\/h5>\n<div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><\/form><div class=\"teachpress_message_error\"><p>Sorry, no publications matched your criteria.<\/p><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Other Research Areas Expand List Smart Grid Cyber-Physical Systems Multimedia &#8230;<\/p>\n","protected":false},"author":1,"featured_media":999,"parent":9,"menu_order":4,"comment_status":"open","ping_status":"open","template":"","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"class_list":["post-361","page","type-page","status-publish","has-post-thumbnail","hentry"],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/PfR3Ra-5P","_links":{"self":[{"href":"https:\/\/www.comm.utoronto.ca\/dkundur\/wp-json\/wp\/v2\/pages\/361","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.comm.utoronto.ca\/dkundur\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.comm.utoronto.ca\/dkundur\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.comm.utoronto.ca\/dkundur\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.comm.utoronto.ca\/dkundur\/wp-json\/wp\/v2\/comments?post=361"}],"version-history":[{"count":27,"href":"https:\/\/www.comm.utoronto.ca\/dkundur\/wp-json\/wp\/v2\/pages\/361\/revisions"}],"predecessor-version":[{"id":1467,"href":"https:\/\/www.comm.utoronto.ca\/dkundur\/wp-json\/wp\/v2\/pages\/361\/revisions\/1467"}],"up":[{"embeddable":true,"href":"https:\/\/www.comm.utoronto.ca\/dkundur\/wp-json\/wp\/v2\/pages\/9"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.comm.utoronto.ca\/dkundur\/wp-json\/wp\/v2\/media\/999"}],"wp:attachment":[{"href":"https:\/\/www.comm.utoronto.ca\/dkundur\/wp-json\/wp\/v2\/media?parent=361"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}