一类Bogdanov-Takens系统在分段多项式扰动下极限环个数的估计  

Estimation of the number of limit cycles on a class of Bogdanov-Takens systems under piecewise polynomial perturbation

作　　者：晏兵川 李宝毅[1] 张永康[1] YAN Bingchuan;LI Baoyi;ZHANG Yongkang(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2021年第5期1-7,共7页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11271046,11671040);天津师范大学博士基金资助项目(52XB1414).

摘　　要：将平面分为上下2个区域,考虑Bogdanov-Takens系统的非连续分段n(n∈N^(+))次多项式扰动.根据Picard-Fuchs方程组构造二阶微分算子,运用广义Rolle定理估计扰动系统一阶Melnikov函数M_(1)(h)的孤立零点个数,证明了当M_(1)(h)≠0时,扰动系统的极限环个数不超过7n+[n-1/2](计重数).The Bogdanov-Takens systems perturbed by discontinuous piecewise n-degree(n∈N^(+))polynomial is considered when the plane is divided into upper and lower regions.The second-order differential operator is constructed according to the Picard-Fuchs equations.The number of isolated zero of the first-order Melnikov function M_(1)(h)is estimated by the generalized Rolle theorem,and it is proved that when M_(1)(h)≠0,the number of limit cycles of disturbed systems is no more than 7n+[n-1/2],taking account the multiple.

关 键 词：BOGDANOV-TAKENS系统 Picard-Fuchs方程组 二阶微分算子 极限环 

分 类 号：O175[理学—数学]