【摘要】 研究两类BiLiénard系统的中心条件与极限环分支问题。在适当的变换下,将两类BiLiénard系统转化成与之相对应的伴随复系统。通过计算三次和五次BiLiénard系统在原点处的前3个和前7个奇点量,得到了原点成为最高阶细奇点和中心的条件,证明了这两类系统在原点小邻域内能产生3个和7个小振幅极限环。更多还原

【Abstract】 The center conditions and bifurcations of limit cycles for two classes of BiLiénard systems are investigated. Under the suitable conditions,the considered systems are first transformed into the corresponding complex concomitant systems. Then the conditions of the origin to be the highest order weak critical singular point and to be a center are deduced by computing the first three and seven singular point quantities for cubic and quintic BiLiénard system,respectively. Finally,it is proven that these systems can generate 3 and 7 small amplitude limit cycles in the small neighborhood of the origin,respectively.更多还原