{"id":13,"date":"2013-10-23T15:32:33","date_gmt":"2013-10-23T15:32:33","guid":{"rendered":"http:\/\/localhost:8888\/?page_id=13"},"modified":"2018-03-29T09:40:07","modified_gmt":"2018-03-29T07:40:07","slug":"research","status":"publish","type":"page","link":"http:\/\/users.dimi.uniud.it\/~dimitri.breda\/research\/","title":{"rendered":"research"},"content":{"rendered":"<p style=\"text-align: justify\">My research interests focus around dynamical systems generated by retarded functional equations. What does &#8220;retarded&#8221; mean? Well, the question should be whether the future depends only on the present or also on the past.<\/p>\n<p style=\"text-align: justify\">Mathematically speaking, delay means an infinite-dimensional state space. Hence no surprise that, soon or later, one has to resort to numerical analysis. What for? Not just to compute a solution, but rather to investigate stability of equilibria and periodic orbits, or chaotic attractors.<\/p>\n<p style=\"text-align: justify\">In particular, I mainly work on numerical methods to approximate the spectra of those operators governing the linearized dynamics. Examples are solution operators, infinitesimal generators, monodromy operators and evolution families. Yes, there is a bit of functional analysis behind.<\/p>\n<p style=\"text-align: justify\">The application fields I deal with are relevant to models of epidemics or physiologically structured populations (consumer-resource dynamics, age-dependent populations) and problems of control arising in mechanical engineering (Mathieu equations) or similar (networks). Translated, I am talking about functional equations which can be with delay or advanced-retarded, of neutral type, simply differential or integro-differential, or even couplings of the latter.<\/p>\n<p>To know more, visit the other pages.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>My research interests focus around dynamical systems generated by retarded functional equations. What does &#8220;retarded&#8221; mean? Well, the question should be whether the future depends only on the present or also on the past. Mathematically speaking, delay means an infinite-dimensional state space. Hence no surprise that, soon or later, one has to resort to numerical [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"class_list":["post-13","page","type-page","status-publish","hentry"],"jetpack_shortlink":"https:\/\/wp.me\/P49dE6-d","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/users.dimi.uniud.it\/~dimitri.breda\/wp-json\/wp\/v2\/pages\/13","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/users.dimi.uniud.it\/~dimitri.breda\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/users.dimi.uniud.it\/~dimitri.breda\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/users.dimi.uniud.it\/~dimitri.breda\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/users.dimi.uniud.it\/~dimitri.breda\/wp-json\/wp\/v2\/comments?post=13"}],"version-history":[{"count":27,"href":"http:\/\/users.dimi.uniud.it\/~dimitri.breda\/wp-json\/wp\/v2\/pages\/13\/revisions"}],"predecessor-version":[{"id":458,"href":"http:\/\/users.dimi.uniud.it\/~dimitri.breda\/wp-json\/wp\/v2\/pages\/13\/revisions\/458"}],"wp:attachment":[{"href":"http:\/\/users.dimi.uniud.it\/~dimitri.breda\/wp-json\/wp\/v2\/media?parent=13"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}