{"id":132529,"date":"2024-08-29T13:06:56","date_gmt":"2024-08-29T10:06:56","guid":{"rendered":"https:\/\/azbuki.bg\/?p=132529"},"modified":"2024-08-29T13:06:56","modified_gmt":"2024-08-29T10:06:56","slug":"dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory","status":"publish","type":"post","link":"https:\/\/vocedu.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/","title":{"rendered":"Dynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory"},"content":{"rendered":"

Nikolay Kyurkchiev1,2), Tsvetelin Zaevski2,3)<\/strong>
\nAnton Iliev1,2), Vesselin Kyurkchiev1), Asen Rahnev1)<\/strong>
\nUniversity of Plovdiv \u201ePaisii Hilendarski\u201c (Bulgaria)<\/em>
\n2)Institute of Mathematics and Informatics,<\/em>
\nBulgarian Academy of Sciences (Bulgaria)<\/em>
\n3)Faculty of Mathematics and Informatics,<\/em>
\nSofia University \u201cSt. Kliment Ohridski\u201d (Bulgaria)<\/em><\/p>\n

https:\/\/doi.org\/10.53656\/math2024-4-1-dyn<\/a><\/p>\n

Abstract.<\/strong> In this paper, we propose a new class of extended oscillators. Some investigations based on the Melnikov\u2019s approach are applied for identifying some chaotic possibilities. We demonstrate also some specialized modules for investigating the dynamics of these oscillators. One possible application that Melnikov functions may find in the modeling and synthesis of radiating antenna patterns is also discussed. This will be included as an integral part of a planned much more general Web-based application for scientific computing.
\nKeywords:<\/em> escape oscillator, Melnikov\u2019s method, hypothetical Melnikov antenna array<\/p>\nLog in to read the full text<\/a>","protected":false},"excerpt":{"rendered":"

Nikolay Kyurkchiev1,2), Tsvetelin Zaevski2,3) Anton Iliev1,2), Vesselin Kyurkchiev1), Asen Rahnev1) University of Plovdiv \u201ePaisii Hilendarski\u201c (Bulgaria) 2)Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (Bulgaria) 3)Faculty of Mathematics and Informatics, Sofia University \u201cSt. Kliment Ohridski\u201d (Bulgaria) https:\/\/doi.org\/10.53656\/math2024-4-1-dyn Abstract. In this paper, we propose a new class of extended oscillators. Some investigations based on the […]<\/p>","protected":false},"author":124332423427287,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":{"source_name":"","source_url":"","via_name":"","via_url":"","override_template":"0","override":[{"template":"1","single_blog_custom":"","parallax":"1","fullscreen":"1","layout":"right-sidebar","sidebar":"default-sidebar","second_sidebar":"default-sidebar","sticky_sidebar":"1","share_position":"bottom","share_float_style":"share-monocrhome","show_share_counter":"1","show_view_counter":"1","show_featured":"0","show_post_meta":"1","show_post_author":"1","show_post_author_image":"1","show_post_date":"1","post_date_format":"custom","post_date_format_custom":"d-m-Y","show_post_category":"1","show_post_reading_time":"0","post_reading_time_wpm":"300","show_zoom_button":"1","zoom_button_out_step":"2","zoom_button_in_step":"3","show_post_tag":"1","show_prev_next_post":"1","show_popup_post":"1","number_popup_post":"3","show_author_box":"0","show_post_related":"0","show_inline_post_related":"0"}],"override_image_size":"0","image_override":[{"single_post_thumbnail_size":"crop-500","single_post_gallery_size":"crop-500"}],"trending_post":"0","trending_post_position":"meta","trending_post_label":"Trending","sponsored_post":"0","sponsored_post_label":"Sponsored by","sponsored_post_name":"","sponsored_post_url":"","sponsored_post_logo_enable":"0","sponsored_post_logo":"","sponsored_post_desc":"","disable_ad":"0"},"jnews_primary_category":{"id":"","hide":""}},"categories":[1],"tags":[7582,7584,7583],"yoast_head":"\nDynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Dynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"Nikolay Kyurkchiev1,2), Tsvetelin Zaevski2,3) Anton Iliev1,2), Vesselin Kyurkchiev1), Asen Rahnev1) University of Plovdiv \u201ePaisii Hilendarski\u201c (Bulgaria) 2)Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (Bulgaria) 3)Faculty of Mathematics and Informatics, Sofia University \u201cSt. Kliment Ohridski\u201d (Bulgaria) https:\/\/doi.org\/10.53656\/math2024-4-1-dyn Abstract. In this paper, we propose a new class of extended oscillators. Some investigations based on the […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Azbuki55\/\" \/>\n<meta property=\"article:published_time\" content=\"2024-08-29T10:06:56+00:00\" \/>\n<meta name=\"author\" content=\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/\"},\"author\":{\"name\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd\"},\"headline\":\"Dynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory\",\"datePublished\":\"2024-08-29T10:06:56+00:00\",\"dateModified\":\"2024-08-29T10:06:56+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/\"},\"wordCount\":176,\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"keywords\":[\"escape oscillator\",\"hypothetical Melnikov antenna array\",\"Melnikov\u2019s method\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/\",\"url\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/\",\"name\":\"Dynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory - \u0410\u0437-\u0431\u0443\u043a\u0438\",\"isPartOf\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#website\"},\"datePublished\":\"2024-08-29T10:06:56+00:00\",\"dateModified\":\"2024-08-29T10:06:56+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/strategies.azbuki.bg\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Dynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#website\",\"url\":\"https:\/\/vocedu.azbuki.bg\/en\/\",\"name\":\"\u0410\u0437-\u0431\u0443\u043a\u0438\",\"description\":\"\u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0438\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e \u0437\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u043d\u0430\u0443\u043a\u0430\",\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/vocedu.azbuki.bg\/en\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\",\"name\":\"\u0410\u0437-\u0431\u0443\u043a\u0438\",\"url\":\"https:\/\/vocedu.azbuki.bg\/en\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png\",\"contentUrl\":\"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png\",\"width\":250,\"height\":70,\"caption\":\"\u0410\u0437-\u0431\u0443\u043a\u0438\"},\"image\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/Azbuki55\/\",\"https:\/\/www.instagram.com\/nion_azbuki\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd\",\"name\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g\",\"caption\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\"},\"sameAs\":[\"https:\/\/azbuki.bg\/\"],\"url\":\"https:\/\/vocedu.azbuki.bg\/en\/author\/azbuki_ekip\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Dynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory - \u0410\u0437-\u0431\u0443\u043a\u0438","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/","og_locale":"en_US","og_type":"article","og_title":"Dynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory - \u0410\u0437-\u0431\u0443\u043a\u0438","og_description":"Nikolay Kyurkchiev1,2), Tsvetelin Zaevski2,3) Anton Iliev1,2), Vesselin Kyurkchiev1), Asen Rahnev1) University of Plovdiv \u201ePaisii Hilendarski\u201c (Bulgaria) 2)Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (Bulgaria) 3)Faculty of Mathematics and Informatics, Sofia University \u201cSt. Kliment Ohridski\u201d (Bulgaria) https:\/\/doi.org\/10.53656\/math2024-4-1-dyn Abstract. In this paper, we propose a new class of extended oscillators. Some investigations based on the […]","og_url":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/","og_site_name":"\u0410\u0437-\u0431\u0443\u043a\u0438","article_publisher":"https:\/\/www.facebook.com\/Azbuki55\/","article_published_time":"2024-08-29T10:06:56+00:00","author":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","twitter_card":"summary_large_image","twitter_misc":{"Written by":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/#article","isPartOf":{"@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/"},"author":{"name":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd"},"headline":"Dynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory","datePublished":"2024-08-29T10:06:56+00:00","dateModified":"2024-08-29T10:06:56+00:00","mainEntityOfPage":{"@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/"},"wordCount":176,"publisher":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#organization"},"keywords":["escape oscillator","hypothetical Melnikov antenna array","Melnikov\u2019s method"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/","url":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/","name":"Dynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory - \u0410\u0437-\u0431\u0443\u043a\u0438","isPartOf":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#website"},"datePublished":"2024-08-29T10:06:56+00:00","dateModified":"2024-08-29T10:06:56+00:00","breadcrumb":{"@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/dynamics-of-a-new-class-of-oscillators-melnikovs-approach-possible-application-to-antenna-array-theory\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/strategies.azbuki.bg\/"},{"@type":"ListItem","position":2,"name":"Dynamics of a New Class of Oscillators: Melnikov\u2019s Approach, Possible Application to Antenna Array Theory"}]},{"@type":"WebSite","@id":"https:\/\/vocedu.azbuki.bg\/en\/#website","url":"https:\/\/vocedu.azbuki.bg\/en\/","name":"\u0410\u0437-\u0431\u0443\u043a\u0438","description":"\u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0438\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e \u0437\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u043d\u0430\u0443\u043a\u0430","publisher":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/vocedu.azbuki.bg\/en\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/vocedu.azbuki.bg\/en\/#organization","name":"\u0410\u0437-\u0431\u0443\u043a\u0438","url":"https:\/\/vocedu.azbuki.bg\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/","url":"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png","contentUrl":"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png","width":250,"height":70,"caption":"\u0410\u0437-\u0431\u0443\u043a\u0438"},"image":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/Azbuki55\/","https:\/\/www.instagram.com\/nion_azbuki\/"]},{"@type":"Person","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd","name":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g","caption":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c"},"sameAs":["https:\/\/azbuki.bg\/"],"url":"https:\/\/vocedu.azbuki.bg\/en\/author\/azbuki_ekip\/"}]}},"_links":{"self":[{"href":"https:\/\/vocedu.azbuki.bg\/en\/wp-json\/wp\/v2\/posts\/132529"}],"collection":[{"href":"https:\/\/vocedu.azbuki.bg\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vocedu.azbuki.bg\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vocedu.azbuki.bg\/en\/wp-json\/wp\/v2\/users\/124332423427287"}],"replies":[{"embeddable":true,"href":"https:\/\/vocedu.azbuki.bg\/en\/wp-json\/wp\/v2\/comments?post=132529"}],"version-history":[{"count":1,"href":"https:\/\/vocedu.azbuki.bg\/en\/wp-json\/wp\/v2\/posts\/132529\/revisions"}],"predecessor-version":[{"id":132531,"href":"https:\/\/vocedu.azbuki.bg\/en\/wp-json\/wp\/v2\/posts\/132529\/revisions\/132531"}],"wp:attachment":[{"href":"https:\/\/vocedu.azbuki.bg\/en\/wp-json\/wp\/v2\/media?parent=132529"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vocedu.azbuki.bg\/en\/wp-json\/wp\/v2\/categories?post=132529"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vocedu.azbuki.bg\/en\/wp-json\/wp\/v2\/tags?post=132529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}