一类平面九次微分系统的广义中心条件与极限环分支

General center conditions and bifurcation of limit cycles for a planar differential system of nine degrees

文中着力于研究一类平面九次微分系统的广义中心条件与极限环分支,通过进行2个合适的变换和对李雅普诺夫常数即焦点量的仔细计算和化简,得到该系统的无穷远点和4个初等奇点成为同步中心的条件,进一步讨论了其同步极限环分支问题,得出该系统在一定的扰动下可以同时分支出15个极限环的结论。这15个极限环中,3个为大振幅极限环,12个小振幅极限环。

This paper concerned with a class of planar differential system of nine degrees.By making two appropriate transformations of system and calculating focal values carefully,the conditions for the infinity point and four elementary singularities of the system to be isochronous centers were obtained.Furthermore,the bifurcation of the limit cycle of the system was discussed.It is concluded that 15 limit cycles can be bifurcated simultaneously under certain perturbation.Among these 15 limit cycles,3 are large amplitude limit cycles and 12 are small amplitude limit cycles.