摘要
给出了一类二阶非线性保守系统周期轨道族与同异宿轨道显式表示的初等积分方法;同时指出:根据周期轨道族外围分界线环类型的不同,周期轨道族需由不同的Jacobian椭圆函数来表示并揭示了其中的原因.利用文中方法,通过变量替换,旋转以及积分因子等手段,可推导获得某些更复杂非线性系统周期轨道族与同异宿轨道的显式式.因此所得结果对于非线性(扰动)系统分支与混沌的研究有帮助.
The elementary integration method for deriving the explicit representations of periodic orbits families and homoclinic and heteroclinic orbits in a second-order nonlinear conservative system is given. It is pointed out that, according to the different separatrixes of periodic orbits families, the different Jacobian elliptic functions should be used. The associated reasons are revealed. Utilizing the method in this paper, the explicit representations of periodic orbits families and homoclinic and hete- roclinic orbits in some more complex nonlinear systems can be obtained through changes of variables, rotations and integral factors, etc. Thus, the results chaos in nonlinear systems under perturbations. in this paper benefit the study of bifurcations and
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2012年第4期390-398,共9页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(11102041)
中国博士后科学基金(2011M500803)
福建省教育厅A类项目(JA10065)
关键词
非线性保守系统
周期轨
同异宿轨
显式表示
Jacobian椭圆函数
nonlinear conservative systems
periodic orbits
homoclinic and heteroclinic orbits explicit representations
Jacobian elliptic functions
