{"id":2494,"date":"2014-12-10T23:56:18","date_gmt":"2014-12-10T21:56:18","guid":{"rendered":"http:\/\/www.rsijournal.eu\/?p=2494"},"modified":"2021-01-20T13:22:32","modified_gmt":"2021-01-20T11:22:32","slug":"optimization-of-deterministic-population-dynamics-models","status":"publish","type":"post","link":"https:\/\/rsijournal.eu\/?p=2494","title":{"rendered":"OPTIMIZATION OF DETERMINISTIC POPULATION DYNAMICS MODELS"},"content":{"rendered":"<p><strong>Michaela BENE\u0160OV\u00c1<\/strong><br \/>\nDepartment of Mathematics and Statistics of the Faculty of Science, Masaryk University<br \/>\nKotl\u00e1\u0159sk\u00e1 2, 611 37 Brno Czech Republic<br \/>\nmisasula@gmail.com<\/p>\n<p><strong>Abstract<\/strong><br \/>\nThe aim of this contribution is to apply methods from optimal control theory to the mathematical modeling of biological pest control. We formulate a pest control strategy for nonlinear Kolmogorov system of n interacting populations by introducing natural enemies as a control function. The sufficient conditions for existence of an optimal feedback control function are based on the fact, that the steady-state solution of the Hamilton-Jacobi-Bellman partial differential equation is a Lyapunov function guaranteeing stability and optimality. We apply those general results to the Lotka-Volterra system with a logistic rate of increase of the prey population and Holling\u2019s second type functional response of the predator population, to illustrate biological control of pest mite in stored grain Acarus siro by predatory mite Cheyletus eruditus.<\/p>\n<p><em><a href=\"http:\/\/www.rsijournal.eu\/ARTICLES\/December_2014\/3.pdf\" target=\"_blank\" rel=\"noopener\">read more<\/a><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Michaela BENE\u0160OV\u00c1 Department of Mathematics and Statistics of the Faculty of Science, Masaryk University Kotl\u00e1\u0159sk\u00e1 2, 611 37 Brno Czech Republic misasula@gmail.com Abstract The aim of this contribution is to apply methods from optimal control theory to the mathematical modeling of biological pest control. We formulate a pest control strategy for nonlinear Kolmogorov system of&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[181,1],"tags":[],"class_list":["post-2494","post","type-post","status-publish","format-standard","hentry","category-published","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/rsijournal.eu\/index.php?rest_route=\/wp\/v2\/posts\/2494","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rsijournal.eu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rsijournal.eu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rsijournal.eu\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/rsijournal.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2494"}],"version-history":[{"count":3,"href":"https:\/\/rsijournal.eu\/index.php?rest_route=\/wp\/v2\/posts\/2494\/revisions"}],"predecessor-version":[{"id":3836,"href":"https:\/\/rsijournal.eu\/index.php?rest_route=\/wp\/v2\/posts\/2494\/revisions\/3836"}],"wp:attachment":[{"href":"https:\/\/rsijournal.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rsijournal.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rsijournal.eu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}