پديد آورنده :
علي عبدالعباس البياتي، زينب
عنوان :
انشعاب سيكل هاي حدي براي دستگاه مسطح مرتبه سه حول يك نقطه تكين پوچ توان
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
صفحه شمار :
هشت، ۹۲ص.: مصور
استاد راهنما :
حميدرضا ظهوري زنگنه
واژه نامه :
انگليسي به فارسي ; فارسي به انگليسي
توصيفگر ها :
نقطه تعادل پوچ توان , ثابت لياپانف تعميم يافته , ساده ترين فرم نرمال , سيكل حدي
استاد داور :
محمود منجگاني، رسول كاظمي
تاريخ ورود اطلاعات :
1397/10/10
چكيده انگليسي :
Bifurcation of limit cycles in a cubic order planar system around a nilpotent critical point Zainab Ali Abdulabass al Bayti zainabalbroojordy@gmail com September 22 2018 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid Reza Zohouri Zangeneh hamidz@cc iut ac ir 2010 MSC 34C07 37G15 Keywords Nilpotent singularity Generalized Lyapunov constant The simplest normal form Limit cycle AbstractIn this thesis based on paper 61 bifurcation of limit cycles is considered for planar cubic ordersystems with an isolated nilpotent critical point Normal form theory is applied to compute thegeneralized Lyapunov constants and to prove the existence of at least 9 small amplitude limit cyclesin the neighborhood of the nilpotent critical point In addition the method of double bifurcation ofnilpotent focus is used to show that such systems can have up to 10 small amplitude limit cycles nearthe nilpotent critical point These are new lower bounds on the number of limit cycles in planar cubic order systems near an isolated nilpotent critical point Moreover a set of center conditions is obtainedfor such cubic systems Dynamical systems can exhibit self sustained oscillations called limit cycles which may appear in almost all fields of science and engineering Developing limit cycle theory is notonly theoretically significant but also practically important Limit cycles theory is closely related tothe well known Hilbert s 16th problem one of the 23 mathematical problems proposed by D Hilbertin 1900 A modern version of this problem was included in the 18 most challenging mathematicalproblems proposed by S Smale for the 21st century Consider the following planar differential system dx dy 4 48 Pn x y Qn x y dt dt
استاد راهنما :
حميدرضا ظهوري زنگنه
استاد داور :
محمود منجگاني، رسول كاظمي
