具有积分因子的平面多项式系统的极限环个数  

The number of limit cycles of a planar polynomial system with integrating factors

作　　者：白龙 BAI Long(School of Mathematics and Computer Science,Ningxia Normal University,Guyuan Ningxia 756099)

机构地区：[1]宁夏师范大学数学与计算机科学学院,宁夏固原756099

出　　处：《宁夏师范学院学报》2024年第10期39-45,94,共8页Journal of Ningxia Normal University

基　　金：宁夏自然科学基金项目(2022AAC03333).

摘　　要：应用Melnikov函数法,研究一类具有积分因子的平面多项式系统在2次多项式扰动下极限环的最大个数问题.推导系统的一阶Melnikov函数的表达式,得到系统的一阶Melnikov函数恒为0;然后探讨系统的二阶Melnikov函数,得出该系统最多有5个极限环(计重数).该研究结果对于一般具有积分因子的多项式系统的极限环个数研究有一定应用价值.The maximum number of limit cycles for a class of planar polynomial systems with integrating factors under the perturbation of quadratic polynomials is studied using the Melnikov function method.The expression of the first-order Melnikov function for the system is deduced,and it is found to be identically zero.Then,the second-order Melnikov function is explored,and it is concluded that the system can have at most five limit cycles(considering multiplicity).This research has certain application value for the study of the number of limit cycles in general polynomial systems with integrating factors.

关 键 词：平面多项式系统 极限环 Melnikov函数法 积分因子 HILBERT第16问题 

分 类 号：O175[理学—数学]