پديد آورنده :
فتاحي فرادنبه، مريم
عنوان :
مدارهاي تناوبي براي اختلالي از سيستم هاي قطعه اي خطي
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
ده، [107]ص.: مصور، جدول، نمودار
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
حميدرضا ظهوري زنگنه
توصيفگر ها :
منيفلدهاي پايا , تابع ملنيكف , روش معدل گيري
تاريخ نمايه سازي :
94/2/30
استاد داور :
محمدرضا رئوفي، رسول عاشقي
تاريخ ورود اطلاعات :
1396/09/27
چكيده انگليسي :
Periodic orbits for perturbations of piecewise linear systems Maryam Fatahi Fradonbeh m fatahi@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamidreza Zohouri Zangeneh Hamidz@cc iut ac ir Advisor Dr Majid Gazor mgazor@cc iut ac ir 2010 MSC 34C23 34C25 34C45 37G15 Keywords Piecewise linear systems Periodic orbits Invariant manifolds Melnikov function Averaging method AbstractPiecewise linear systems present almost the same dynamical behaviour as that of general nonlinearsystems limit cycles homoclinic and heteroclinic orbits strange attractors In order to carry out a complete study of picewise linear systems some canonical forms have beenintroduced in several works In practice many nonlinear systems can be adequately modelled bycontinuous piecewise linear systems separated by one or two parallel hyperplanes splitting the phasespace in R3 in to di erent linear dynamic regions In this case the canonical forms which takeadvantage of some concepts from classical systems theory are able to cope with such nonlinear systems Even for the simplest case with only one separating hyperplane the state of the art in piecewise linearsystems analysis is not very satisfactory In fact there are no general results about their dynamicalbehavior for instance existence of oscillations bifurcations Thus we are forced to considerspece c cases one by one We consider the existence of periodic orbits in a class of three dimensional continuouse piecewise linearsystem with only two zones hereafter 2CP L3 systems A very useful strategy to capture the richnessof the dynamical behaviour of a nonlinear system consists of looking for its degenerate situations Firstly we describe the dynamical behavior of a non generic piecewise linear system which has twoequilibria and one two dimensional invariant manifold foliated by periodic orbits Next if possible some systems in the family are described as perturbations of the non generic cases studied and then
استاد راهنما :
حميدرضا ظهوري زنگنه
استاد داور :
محمدرضا رئوفي، رسول عاشقي
