CAJ | 학술논문

讨论一类四次多项式微分系统的中心条件与极限环分支问题.通过对该系统所对应的伴随复系统奇点量的计算及证明,得到系统的原点为中心的充要条件.从奇点量导出焦点量,得到了原点成为6阶细焦点的条件,证明了该系统可从原点领域分支出5个小振幅极限环.
토론일류사차다항식미분계통적중심조건여겁한배분지문제.통과대해계통소대응적반수복계통기점량적계산급증명,득도계통적원점위중심적충요조건.종기점량도출초점량,득도료원점성위6계세초점적조건,증명료해계통가종원점영역분지출5개소진폭겁한배.
In this paper, the bifurcation of limit cycles and conditions of origin to be a center for a quartic polynomial system is investigated. By the computation of the singular point values for the concomitant complex system of the real system, and prove strictly the suffciency for the conditions, we obtain the necessary conditions of origin of system to be a center. The focal values are derived from of the singular points, and the conditions is obtained that the origin to be a 6 order weak focal. Finally, 5 small amplitude limit cycles in the neighborhood of the origin in this system is proved.