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Bifurcations of Limit Cycles for Some Perturbed Polynomial Systems

Author: QiXiaoMei
Tutor: ChenWenCheng
School: Shandong University of Science and Technology
Course: Basic mathematics
Keywords: Hilbert sixteenth problem Abel integral Hamilton system Picard - Fuchs equation Polynomial
CLC: O175.12
Type: Master's thesis
Year: 2008
Downloads: 13
Quote: 0
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Abstract


Determine the Abel integral number of zeros on the boundary, and to determine the number of limit cycles of polynomial perturbations of Hamiltonian vector field is still one of the bifurcation theory today a hot research topic . This paper studies a class of Hamilton perturbed system the Abel integral number of zeros of its bifurcation of limit cycles problem . The paper is divided into four chapters: The first chapter is the introduction, which describes the history , development and current situation of the bifurcation theory , and briefly describes the main work of this paper . Second chapter a Single Center Hamilton reversible system cubic polynomial perturbation , the number of its bifurcation of limit cycles at most 2 . The third chapter discusses a class of quasi - reversible Hamiltonian system the number the quartic polynomial perturbations of limit cycles branch , its least upper bound is to promote Zhao Yulin [ 43 ] results . Chapter we consider a class with parameters Hamilton Bifurcation of Limit Cycles quartic polynomial perturbations of the system can produce up to 12 limit cycle to promote Zhang Tonghua , Chen Wencheng et al [ 38 ] results .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Ordinary Differential Equations > Qualitative theory
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