شماره راهنما :
1596 دكتري
پديد آورنده :
موسوي، مرضيه
عنوان :
انشعاب سيكل هاي حدي در دستگاه هاي نزديك به انتگرال پذير
گرايش تحصيلي :
رياضي كاربردي (دستگاه هاي ديناميكي)
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
صفحه شمار :
نه، 125ص. : مصور
استاد راهنما :
حميدرضا ظهوري زنگنه
استاد مشاور :
رسول كاظمي نجف آبادي
توصيفگر ها :
سيكل حدي , مسأله شانزدهم هيلبرت , انشعاب , دستگاه هميلتوني , حلقه هموكلينيك , حلقه هتروكلينيك , پلي‌سيكل , تابع ملنيكف , فشرده‌سازي پوانكاره , نماي فاز , ديسك پوانكاره
استاد داور :
حسين خيري استيار، رضا خوش سير قاضياني، اعظم اعتماد دهكردي
تاريخ ورود اطلاعات :
1399/05/11
تاريخ ويرايش اطلاعات :
1399/05/11
چكيده انگليسي :
Bifurcation of limit cycles in near integrable systems Marzieh Mousavi marzieh mousavi@math iut ac ir January 1 2020 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamidreza Zohouri Zangeneh hamidz@iut ac ir Advisor Dr Rasool Kazemi r kazemi@kashanu ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Department of Mathematics Faculty of Science University of Kashan Kashan 87317 51167 Iran AbstractA limit cycle is an isolated periodic solutions in the set of all periodic solutions of a system ofdi erential equations Periodic behaviors in the nature often appear as a limit cycle in theircorresponding mathematical models and therefore knowing the number and position of limitcycles are important to understand the dynamical behavior of the system This thesis dealswith bifurcation of limit cycles from planar polynomial near integrable systems Here weuse the asymptotic expansions of the rst order Melnikov function and Chebyshev criterionfor studying bifurcation of limit cycles for small perturbations of some Hamiltonian systemswith n polycyles n 3 in their phase portraits Moreover a new family of centers of planarpolynomial di erential systems of arbitrary even degree is introduced and classi ed the globalphase portraits of the centers of this family having degree 2 4 and 6 in the Poincar disc eAlso we have studied existence or non existence of limit cycles for Higgins Selkov systemand classi ed the phase portraits of these systems in the Poincar disc for di erent values of eparameters Key Words Limit cycle Hilbert s 16th problem Bifurcation Hamiltonian system Ho moclinic loop Heteroclinic loop Polycycle Melnikov function Poincar compacti cation ephase portrait Poincar disk eMSC 2010 34C05 34C07 34C08 37G15 34A05 37C10 Introduction and statement of the main resultsThe second part of the well known Hilbert s 16th problem proposed in 1900 is to nd themaximum number and determine the possible relative positions of limit cycles of the planardi erential system of the form x Pn x y y Qn x y for a given integer n and all possible Pn and Qn where Pn and Qn are real polynomials andthe maximum degree of them is n Despite numerous investigations on this problem it still 1
استاد راهنما :
حميدرضا ظهوري زنگنه
استاد مشاور :
رسول كاظمي نجف آبادي
استاد داور :
حسين خيري استيار، رضا خوش سير قاضياني، اعظم اعتماد دهكردي
