摘要
研究了一类具有双异宿环的五次哈密尔顿系统x=y,y=-(ax+bx3+cx5)在ε(α+βx2+x4)/y扰动下的分支现象,其中a<0,b>0,3b2=16ac.证明了当0<|ε|1时至多能分支出2个极限环,并且给出了完整的分支图.
Abstract We consider bifurcation of a class of quintic Hamiltonian system x=y,y=-(ax+bx^3+cx^5)with double heteroclinic loops under small perturbation of the form , where a〈0,b〉0 and3b^2=16ac. It is proved that at most 2 limit cycles can be bifurcated for 0〈|ε|〈〈1, and a complete bifurcation diagram is obtained.
出处
《北京师范大学学报(自然科学版)》
CAS
CSCD
北大核心
2012年第6期587-591,共5页
Journal of Beijing Normal University(Natural Science)
基金
国家自然科学基金资助项目(11271046)
the Tundamental Research Funds for the Central Universities
关键词
超椭圆哈密尔顿函数
阿贝尔积分
极限环
hyper-elliptic Hamiltonian function
Abelian integral
limit cycle