{"id":2293,"date":"2022-11-28T14:50:22","date_gmt":"2022-11-28T14:50:22","guid":{"rendered":"http:\/\/journal.ziu-university.net\/?p=2293"},"modified":"2022-11-28T14:50:24","modified_gmt":"2022-11-28T14:50:24","slug":"dynamic-of-the-singularly-perturbed-nicholson-equation","status":"publish","type":"post","link":"https:\/\/journal.ziu.edu.sy\/?p=2293","title":{"rendered":"<strong>Dynamic of the singularly perturbed Nicholson equation<\/strong>"},"content":{"rendered":"\n<p class=\"has-text-align-left wp-block-paragraph\"> : <strong>Abstract<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">In this paper, we consider a class of singularly perturbed equations with a parameter. By letting the perturbation parameter tends to zero, such an equation is formally reduced to a scalar difference equation. Local stability analysis of fixed points is investigated. The method of steps is used to discretize the system. Moreover, Numerical simulations including Lyapunov exponent, bifurcation and chaos is carried out to confirm the theoretical analysis obtained to explore more complex dynamic of the system<\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\"><strong>Keywords: <\/strong>\u00a0Fixed points, Local stability, Lyapunov exponent, Bifurcation and Chaos.<\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">: make it by<\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">Neamaa A. Elabd<\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">Faculty of Science, Derna University, Libya.<\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">&amp;<\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">Masouda&nbsp; M. A. Al-Fadel<\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">Faculty of Science, Derna University, Libya.<\/p>\n\r\n\t\t<div class=\"review_wrap\">\r\n\t\t\t<div id=\"review-box\" class=\"review-box review-bottom review-stars\">\r\n\t\t\t\t<div class=\"review-summary\">\r\n\t\t\t\t\t<div class=\"review-final-score\">\r\n\t\t\t\t\t\t<span title=\"\" class=\"post-large-rate stars-large\"><span style=\"width:0%\"><\/span><\/span>\r\n\t\t\t\t\t\t<h4><\/h4>\r\n\t\t\t\t\t<\/div>\r\n\t\t\t\t\r\n\t\t\t\t<div class=\"review-short-summary\"><a href=\"https:\/\/drive.google.com\/file\/d\/1PlOZ8ap3i-zacEb7wTTIH_QnOPlH_YEm\/view?usp=sharing\" class=\"taq-button taq-medium taq-square taq-flat\" style=\"background-color:#a0ce4e\" target=\"_blank\"><i class=\"fa fa-download\"><\/i><span class=\"button-text\">\u062a\u062d\u0645\u064a\u0644<\/span><\/a>\r\n\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t\t\r\n\t\t\t<div class=\"user-rate-wrap\">\r\n\t\t\t\t<span class=\"user-rating-text\">\r\n\t\t\t\t\t<strong>\u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0648\u0646: <\/strong>\r\n\t\t\t\t\t<span class=\"taq-score\"><\/span>\r\n\t\t\t\t\t<small>\u0643\u0646 \u0623\u0648\u0644 \u0627\u0644\u0645\u0635\u0648\u062a\u0648\u0646 !<\/small>\r\n\t\t\t\t<\/span>\r\n\r\n\t\t\t\t<div data-rate=\"0\" data-id=\"2293\" class=\"user-rate taq-user-rate-active\">\r\n\t\t\t\t\t<span class=\"user-rate-image post-large-rate stars-large\">\r\n\t\t\t\t\t\t<span style=\"width:0%\"><\/span>\r\n\t\t\t\t\t<\/span>\r\n\t\t\t\t<\/div>\r\n\r\n\t\t\t\t<div class=\"taq-clear\"><\/div>\r\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>","protected":false},"excerpt":{"rendered":"<p>: Abstract In this paper, we consider a class of singularly perturbed equations with a parameter. By letting the perturbation parameter tends to zero, such an equation is formally reduced to a scalar difference equation. Local stability analysis of fixed points is investigated. The method of steps is used to discretize the system. Moreover, Numerical &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[75],"tags":[],"class_list":["post-2293","post","type-post","status-publish","format-standard","","category-75"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\r\n<title>Dynamic of the singularly perturbed Nicholson equation - \u0645\u062c\u0644\u0629 \u062c\u0627\u0645\u0639\u0629 \u0627\u0644\u0632\u064a\u062a\u0648\u0646\u0629 \u0627\u0644\u062f\u0648\u0644\u064a\u0629 \u0644\u0644\u0646\u0634\u0631 \u0627\u0644\u0639\u0644\u0645\u064a<\/title>\r\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\r\n<link rel=\"canonical\" href=\"https:\/\/journal.ziu.edu.sy\/?p=2293\" \/>\r\n<meta property=\"og:locale\" content=\"ar_AR\" \/>\r\n<meta property=\"og:type\" content=\"article\" \/>\r\n<meta property=\"og:title\" content=\"Dynamic of the singularly perturbed Nicholson equation - \u0645\u062c\u0644\u0629 \u062c\u0627\u0645\u0639\u0629 \u0627\u0644\u0632\u064a\u062a\u0648\u0646\u0629 \u0627\u0644\u062f\u0648\u0644\u064a\u0629 \u0644\u0644\u0646\u0634\u0631 \u0627\u0644\u0639\u0644\u0645\u064a\" \/>\r\n<meta property=\"og:description\" content=\": Abstract In this paper, we consider a class of singularly perturbed equations with a parameter. By letting the perturbation parameter tends to zero, such an equation is formally reduced to a scalar difference equation. Local stability analysis of fixed points is investigated. The method of steps is used to discretize the system. Moreover, Numerical &hellip;\" \/>\r\n<meta property=\"og:url\" content=\"https:\/\/journal.ziu.edu.sy\/?p=2293\" \/>\r\n<meta property=\"og:site_name\" content=\"\u0645\u062c\u0644\u0629 \u062c\u0627\u0645\u0639\u0629 \u0627\u0644\u0632\u064a\u062a\u0648\u0646\u0629 \u0627\u0644\u062f\u0648\u0644\u064a\u0629 \u0644\u0644\u0646\u0634\u0631 \u0627\u0644\u0639\u0644\u0645\u064a\" \/>\r\n<meta property=\"article:published_time\" content=\"2022-11-28T14:50:22+00:00\" \/>\r\n<meta property=\"article:modified_time\" content=\"2022-11-28T14:50:24+00:00\" \/>\r\n<meta name=\"author\" content=\"admin\" \/>\r\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\r\n<meta name=\"twitter:label1\" content=\"\u0643\u064f\u062a\u0628 \u0628\u0648\u0627\u0633\u0637\u0629\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u0648\u0642\u062a \u0627\u0644\u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u064f\u0642\u062f\u0651\u0631\" \/>\n\t<meta name=\"twitter:data2\" content=\"\u062f\u0642\u064a\u0642\u0629 \u0648\u0627\u062d\u062f\u0629\" \/>\r\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/journal.ziu.edu.sy\\\/?p=2293#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/journal.ziu.edu.sy\\\/?p=2293\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\\\/\\\/journal.ziu.edu.sy\\\/#\\\/schema\\\/person\\\/73a3c191f058bdb2d01e5ae43eb65dba\"},\"headline\":\"Dynamic of the singularly perturbed Nicholson equation\",\"datePublished\":\"2022-11-28T14:50:22+00:00\",\"dateModified\":\"2022-11-28T14:50:24+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/journal.ziu.edu.sy\\\/?p=2293\"},\"wordCount\":119,\"commentCount\":0,\"articleSection\":[\"\u0627\u0644\u0639\u062f\u062f \u0627\u0644\u062b\u0627\u0644\u062b\"],\"inLanguage\":\"ar\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/journal.ziu.edu.sy\\\/?p=2293#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/journal.ziu.edu.sy\\\/?p=2293\",\"url\":\"https:\\\/\\\/journal.ziu.edu.sy\\\/?p=2293\",\"name\":\"Dynamic of the singularly perturbed Nicholson equation - 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