{"id":149024,"date":"2025-04-04T11:45:58","date_gmt":"2025-04-04T08:45:58","guid":{"rendered":"https:\/\/azbuki.bg\/?p=149024"},"modified":"2025-09-17T14:27:57","modified_gmt":"2025-09-17T11:27:57","slug":"a-note-on-a-generalized-dynamical-system-occurs-in-modelling-the-battle-of-the-sexes-chaos-in-sociobiology","status":"publish","type":"post","link":"https:\/\/newspaper.azbuki.bg\/en\/uncategorized\/a-note-on-a-generalized-dynamical-system-occurs-in-modelling-the-battle-of-the-sexes-chaos-in-sociobiology\/","title":{"rendered":"A Note on a Generalized Dynamical System Occurs in Modelling \u2018The Battle of the Sexes\u2019: Chaos in Sociobiology"},"content":{"rendered":"

Nikolay Kyurkchiev1,2), Anton Iliev1), Vesselin Kyurkchiev1),<\/strong>
\nAngel Golev1), Todorka Terzieva1), Asen Rahnev1)<\/strong>
\n1)University of Plovdiv \u201ePaisii Hilendarski\u201c (Bulgaria)<\/em>
\n2)Institute of Mathematics and Informatics,<\/em>
\nBulgarian Academy of Sciences (Bulgaria)<\/em><\/p>\n

https:\/\/doi.org\/10.53656\/math2025-1-2-ano<\/a><\/p>\n

Abstract.<\/strong> In this paper, we propose a new system that occurs in modelling \u201cthe battle of the sexes\u201d in evolutionary biology (Hofbauer & Sigmund 1988). The existence of a heteroclinic cycle and a continuous family of periodic orbits of the system is established; then the dynamical characteristics of a time-periodic perturbation of the system are investigated. By using the well-known Melnikov\u2019s method, a sufficient condition is obtained for the perturbed system to have a transverse hetero-clinic cycle and hence to possess chaotic behaviour in the sense of Smale. One possible application that Melnikov functions may find in the modelling and synthesis of radiating antenna patterns is considered. We demonstrate some modules for investigating the dynamics of the proposed model. This will be included as an integral part of a planned much more general Web-based application for scientific computing.
\nThe proposed new extended model contains many free parameters (the coefficients ai, i = 1, 2, . . . ,N), which makes it attractive for use in the fields of biological applications, chemistry, sociology, lifetime analysis, reaction kinetics, biostatistics, population dynamic, medical research, games theory etc. Finally, a special case of subharmonic solutions is discussed.<\/p>\n

Keywords:<\/em> new system occurs in modelling \u201cthe battle of the sexes\u201d; hetero-clinic orbit; Melnikov function; subharmonic Melnikov function; chaotic behavior<\/p>\nLog in to read the full text<\/a>","protected":false},"excerpt":{"rendered":"

Nikolay Kyurkchiev1,2), Anton Iliev1), Vesselin Kyurkchiev1), Angel Golev1), Todorka Terzieva1), Asen Rahnev1) 1)University of Plovdiv \u201ePaisii Hilendarski\u201c (Bulgaria) 2)Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (Bulgaria) https:\/\/doi.org\/10.53656\/math2025-1-2-ano Abstract. In this paper, we propose a new system that occurs in modelling \u201cthe battle of the sexes\u201d in evolutionary biology (Hofbauer & Sigmund 1988). 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":[],"jnews_primary_category":[]},"categories":[1],"tags":[10660,10657,10658,10656,10659],"yoast_head":"\nA Note on a Generalized Dynamical System Occurs in Modelling \u2018The Battle of the Sexes\u2019: Chaos in Sociobiology - \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:\/\/azbuki.bg\/en\/uncategorized\/a-note-on-a-generalized-dynamical-system-occurs-in-modelling-the-battle-of-the-sexes-chaos-in-sociobiology\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A Note on a Generalized Dynamical System Occurs in Modelling \u2018The Battle of the Sexes\u2019: Chaos in Sociobiology - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"Nikolay Kyurkchiev1,2), Anton Iliev1), Vesselin Kyurkchiev1), Angel Golev1), Todorka Terzieva1), Asen Rahnev1) 1)University of Plovdiv \u201ePaisii Hilendarski\u201c (Bulgaria) 2)Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (Bulgaria) https:\/\/doi.org\/10.53656\/math2025-1-2-ano Abstract. In this paper, we propose a new system that occurs in modelling \u201cthe battle of the sexes\u201d in evolutionary biology (Hofbauer & Sigmund 1988). 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