پديد آورنده :
شاه سواري نجف آبادي، اسماء
عنوان :
تعداد سيكل هاي حدي يك خانواده از سيستم هاي ليينارد
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
حميدرضا ظهوري زنگنه
توصيفگر ها :
سيستم چند جمله اي ليينارد , انشعاب سراسري , حلقه ي هموكلينيك , حلقه ي هتروكلينيك , تابع ملنيكف
تاريخ نمايه سازي :
11/12/93
استاد داور :
مجيد گازر، رضا مزروعي سبداني
چكيده انگليسي :
On the number of limit cycles of Polynomial Lienard systems Asma Shahsavari Najafabadi a shahsavari@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid Reza Zohouri Zangeneh hamidz@cc iut ac ir Advisor Dr Rasoul Asheghi r asheghi@cc iut ac ir 2010 MSC 37B15 34A34 37A25 94A60 39A33 37D45 Keywords Limit cycle Polynomial Li nard system Global bifurcation Homoclinic loop Hete roclinic loop Melnikov function AbstractLi nard systems are very important mathematical models describing oscillatory processes arising inapplied sciences In this thesis we study polynomial Li nard systems of arbitrary degree on the plane and develop a new method to obtain a lower bound of the maximal number of limit cycles based onpaper Using the method and basing on some known results for lower degrees we obtain a newestimation for the number of limit cycles in these systems which greatly improve existing results Consider a polynomial Li nard system of the form x y y g x f x y where is a small parameter f x and g x are polynomials in x of degree n and m respectively The above system is called a Li nard system It describes the dynamics of systems of one degree offreedom under existence of a linear restoring force and a nonlinear damping It was shown by Li nardthat under some conditions on the functions f x and g x in the system arise auto oscillations In the rst half of the last century models based on the Li nard system were important for thedevelopment of radio and vacuum tube technology Nowadays the system is widely used to describeoscillatory processes arising in various studies of mathematical models of physical biological chemical epidemiological physiological economical and many other phenomena
استاد راهنما :
حميدرضا ظهوري زنگنه
استاد داور :
مجيد گازر، رضا مزروعي سبداني
