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Bifurcation of limit cycles of several types of autonomous differential system

Author: ZuoYuE
Tutor: LiuYiRong
School: Central South University
Course: Applied Mathematics
Keywords: Planar polynomial differential systems Integrability Singular point quantities Infinity Bifurcation of limit cycles
CLC: O175.12
Type: Master's thesis
Year: 2007
Downloads: 22
Quote: 2
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Abstract


This paper studies the planar polynomial differential system origin and the central focus of the point at infinity and integrability conditions with the issue of bifurcation of limit cycles , the text consists of four chapters : Chapter central focus of planar polynomial differential systems judgment overview of the historical background and the research status of the problem and the bifurcation of limit cycles , and this paper simple introduction to the work done . Second chapter studies the amount of saddle point recurrence formula given amount of saddle point of a cubic system integrability conditions , text , and on the computer with Mathematica deduced the first three saddle quantity , its integrable conditions , a careful study further deduce the origin to be the center of conditions , one of the integrability conditions exist integral factor in this article have done a lot of work to get better results present study . The third chapter of a quintic polynomial differential system center conditions and bifurcation of limit cycles infinity problem . Calculated five times infinity point singularity amount linear recurrence formula , use this formula and the computer algebra system Mathematica to calculate the the first ten singularity amount of the infinity point , at the same time to get the point of infinity center conditions and given five points spending seven limit cycles instance . Chapter IV study center conditions and bifurcation of limit cycles in a class there is a small parameter and the origin of the eight ordinary parameters infinity point ( equator ) , obtained by calculating the point of origin and the infinity the Lyapunov constants ( singularity amount ) , the origin and the point at infinity center conditions . Simultaneous perturbation of the point of origin and infinity limit cycle , few studies have been ( 5 ) limit cycle { 3 } and { (3 ) 3} distribution , which is better studied 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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