11525

10588

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

ده، 100ص.: مصور

رسول عاشقي

به فارسي و انگليسي

حميدرضا ظهوري زنگنه، رسول كاظمي

1395/07/18

رياضي

ID10588

Abelian integrals and limit cycles for aclass of cubic polynomial vector fields ofLotka Volterra type with a rational first integral of degree two saeed salehi s753saeed@gmail com 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi r asheghi@cc iut ac ir 2016 MSC 34C05 34A34 34C14 Keywords Limit cycles Abelian integrals Chebyshev criterion Cubic polynomial Vectorfields Simultaneous bifurcation and distribution AbstractThis thesis is based on the paper 4 In this thesis we study the number of limit cycleswhich bifurcate from the periodic orbits of cubic polynomial vector fields of Lotka Volterratype having a rational first integral of degree 2 under polynomial perturbations of degree n The analysis is carried out by estimating the number of zeros of the corresponding Abelianintegrals Moreover using Chebyshev criterion we show that the sharp upper bound forthe number of zeros of the Abelian integrals defined on each period annulus is 3 for n 3 The simultaneous bifurcation and distribution of limit cycles for the system with two periodannuli under cubic polynomial perturbations are considered All configurations u v with0 u v 3 u v 5 are realizable As is known in the study of the qualitative theory ofreal planar differential systems one of the important open problems is the determination oflimit cycles The second part of the famous Hilbert s 16th problem proposed in 1900 asks for

رسول عاشقي

حميدرضا ظهوري زنگنه، رسول كاظمي