摘要
将平面分为左右2个区域,研究Bogdanov-Takens系统在非连续(连续)分段n次多项式扰动下极限环个数的上确界B2(n)(B2c(n)).通过构造二阶微分算子估计一阶Melnikov函数M1(h)(M1c(h))的孤立零点个数的上确界,得到当M1(h)?0(M1c(h)?0)时,在非连续分段多项式扰动下B2(n)≤16n+[n/2]-10,在连续分段多项式扰动下B2c(n)≤16n+[(n-3)/2]-10.
The lowest upper bound B2(n)(B2c(n))of the number of limit cycles on the Bogdanov-Takens system with discontinuous(continuous)piecewise n-degree polynomial perturbation is studied when the plane is divided into left and right domains. By estimating the lowest upper bound of the number of isolated zeros of the first order Melnikov function M1(h)(M1c(h))using the second order differential operator,it is obtained that when M1(h)?0(M1c(h)?0),under the discontinuous piecewise polynomial perturbation,B2(n)≤16 n + [n/2]-10,under the continuous piecewise polynomial perturbation,B2c(n)≤16 n + [(n-3)/2]-10.
作者
崔文喆
李宝毅
张永康
CUI Wenzhe;LI Baoyi;ZHANG Yongkang(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)
出处
《天津师范大学学报（自然科学版）》
CAS
北大核心
2020年第2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).
