8481

7862

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

نه،76ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

رسول عاشقي

محمدرضا رئوفي

8/11/92

حميدرضا ظهوري زنگنه، رضا مزروعي سبداني

رياضي

ID7862

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

abstract Hilbert s th problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in together with the other problems The original problem was posed as the problem of the topology of algebraic curves and surfaces Actually the problem consists of two similar problems in different branches of mathematics An investigation of the relative positions of the branches of real algebraic curves of degree n and similarly for algebraic surfaces The determination of the upper bound for the number of limit cycles in polynomial vector fields of degree n and an investigation of their relative positions indent Usually the maximum of the number of limit cycles is denoted by H n and is called the Hilbert number Recall that a limit cycle is an isolated closed orbit It is the forward or backward limit set of nearby orbits In many application the number and positions of limit cycles are important to understand the dynamical behavior of the system This problem is still open even for the case n Limit cycle behavior is observed in many physical and biological systems As usual we use the notion of the cyclicity for the total number of limit cycles which can emerge from a configuration of trajectories center period annulus a singular loop under a perturbation There are many problems in mechanics electrical engineering and the theory of automatic control which are described by non smooth systems In this thesis we study limit cycle bifurcations for a kind of non smooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with the center at the origin and a homoclinic loop around the origin More precisely we suppose that the unperturbed system dx dt H y dy dt H x Has a family of periodic orbits L h around the origin If h L h approaches the origin which is an elementary center of parabolic focus type And if h L h L where L is a compound homoclinic loop with a saddle S By using the first Melnikov function of piecewise near Hamiltonian systems we give lower bounds of the maximal number of limit cycles in Hopf and homoclinic bifurcations and derive an upper bound of the number of limit cycles that bifurcate from the periodic annulus between the center and the homoclinic loop up to the first order in In the case when the degree of perturbing terms is low we obtain a precise result on the number of zeros of the first Melnikov function PDF created with pdfFactory trial version www pdffactory com

رسول عاشقي

محمدرضا رئوفي

حميدرضا ظهوري زنگنه، رضا مزروعي سبداني