پديد آورنده :
جعفرآبادي، عطيه
عنوان :
انشعاب هاي تاكنز-بوگدانف كند-تند
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
ده،88ص.: مصور،نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
رسول عاشقي
استاد مشاور :
حميدرضا ظهوري زنگنه
توصيفگر ها :
اختلال تكين , سيكل حدي
تاريخ نمايه سازي :
20/1/93
استاد داور :
مجيد گازر، اعظم اعتماد
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Slow fast Bogdanov Takens bifurcations Atiyeh Jafarabadi a jafarabadi@math iut ac ir 18 01 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi r asheghi@cc iut ac ir Advisor Dr Hamid Reza Zohouri Zangeneh hamidz@cc iut ac ir 2010 MSC 34C23 37G10 34C26 Keywords Singular perturbations Bogdanov Takens bifurcation Limit cycles Slow fast AbstractIn this thesis we study perturbations from planar vector elds having a line of zeros and representing asingular limit of Bogdanov Takens BT bifurcations We introduce among other precise de nitions the notion of slow fast BT bifurcation and we provide a complete study of the bifurcation diagramand the related phase portraits Based on geometric singular perturbation theory including blow up we get results that are valid on a uniform neighborhood both in parameter space and in the phaseplane We study the cyclicity of limit periodic sets that occur in families of vector elds of slow fast type The limit periodic sets are formed by a fast orbit and a curve of singularities containing a uniqueturning point At this turning point a stability change takes place on one side of the turning pointthe dynamics point strongly towards the curve of singularities on the other side the dynamics pointaway from the curve of singularities The presence of periodic orbits in a perturbation is relatedto the presence of canard orbits passing near this turning point i e orbits that stay close to thecurve of singularities despite the exponentially strong repulsion near this curve All existing resultsdeal with a non zero slow movement permitting a good estimate of the cyclicity by considering theslow divergence integral along the curve of singularities The most di cult problem to deal with concerns the uniform treatment of the evolution that a limitcycle undergoes when it grows from a small limit cycle near the singular point to a canard cycle ofdetectable size i e a limit cycle that its hausdor limit is not a single point but a canard limitperiodic set or a slow fast cycle
استاد راهنما :
رسول عاشقي
استاد مشاور :
حميدرضا ظهوري زنگنه
استاد داور :
مجيد گازر، اعظم اعتماد
