14477

13062

كارشناسي ارشد

رياضي كاربردي

اصفهان : دانشگاه صنعتي اصفهان

1397

[نه]، 92ص.

حميدرضا ظهوري زنگنه

رسول عاشقي

انگليسي به فارسي; فارسي به انگليسي

محمود منجگاني، رضا مزروعي

1398/01/18

كتابنامه

علوم رياضي

رياضي

1398/01/21

ID13062

The bifurcation analysis of the predator prey systems in various biological models Marjan Eshfagh m eshfagh@math iut ac ir January 15 2019 M Sc Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Hamidreza Zohouri Zangeneh hamidz@math iut ac irAdvisor Dr Rasoul Asheghi r Asheghi@math iut ac irKeywords Hamiltonian system Compactification Poincar sphere Isochronous centerAbstract For a given family of real planar polynomial differential systems depending on parameters one of the mainproblems is the characterization of their centers and their phase portraits The notion of center goes backto Poincare in 25 He defined it for differential systems on the real plane i e a singular point surroundedby ovals of closed orbits with the unique exception of the singular point The classification of the centers of the real polynomial differential systems started with the quadratic oneswith the works of Kapteyn 18 19 Bautin 3 Vulpe 16 Schlomiuk 27 28 and Zoladek in 32 Schlomiuk Guckenheimer and Rand in 29 described a brief history of the problem While the centers and their phase portraits have been characterized for all quadratic polynomial differentialsystems this is not the case for the polynomial differential systems of degree larger than 2 For such systemsthere are only partial results Thus the centers for cubic polynomial differential systems of the form linearplus homogeneous nonlinearities of degree 3 were classified by Malkin and Vulpe and Sibirskii 30 andtheir phase portraits when they are Hamiltonian have been classified by Colak Llibre and Valls in 12 11 Moreover for polynomial differential systems which are linear with homogeneous nonlinearities of degreek 3 the centers are not classified but there are partial results for k 4 5 Chavarriga and Gine 8 9 repectively Nowdays we are very far from obtaining a complete classification of the centers for the class of all cubicpolynomial differential systems of degree 3 In any case some interesting results are given in Rousseau andSchlomiuk 27 and Zoladek 33 Based on the paper by Martin Eduardo Frias Armenta and Jaume Llibre 15 We intend to characterize thephase portraits of the new family of cubic polynomial Hamiltonian differential systems with a center at theorigin and Hamiltonian 1 H x ax2 bxy cy 2 2 y 2 1 2with a2 b2 c2 0 ie of the cubic polynomial Hamiltonian differential systems x y bx 2cy x ax2 bxy cy 2 2 y 1 2ax by x ax2 bxy cy 2 Note that such cubic polynomial differential systems have terms of degree 1 2 and 3 and consequentlyare not studied in the previous mentioned papers dedicated to the centers of cubic polynomial Hamiltoniandifferential systems It is clear that the origin 0 0 is an isolated minimum of the Hamiltonian function H given in 1 andso the origin is a center of the Hamiltonian system 2 because near 0 0 the curves H x y constant areclosed

حميدرضا ظهوري زنگنه

رسول عاشقي

محمود منجگاني، رضا مزروعي