一类Z2对称五次微分系统的中心条件和极限环分支
CENTER CONDITIONS AND BIFURCATIONS OF LIMIT CYCLES FOR A CLASS OF QUINTIC DIFFERENTIAL SYSTEMS WITH Z2 SYMMETRY

本文研究了一类Z2对称五次微分系统的中心条件和小振幅极限环分支.通过前6阶焦点量的计算,获得了原点为中心的充要条件,并证明系统从原点分支出的小振幅极限环的个数至多为6.最后通过构造后继函数,给出系统具有6个围绕原点的小振幅极限环的实例.
In this paper, the center conditions and bifurcations of small amplitude limit cycles for a class of quintic systems with Z2 symmetry are investigated. By the computations of the first six focal quantities, the necessary and sufficient conditions for the origin to be center are derived, and the maximal number of small amplitude limit cycles is proved to be 6. Finally, by constructing displacement function, a concrete example of quintic system is proved to have six small amplitude limit cycles around the origin