一类五次哈密顿系统在四次扰动下的极限环分支

Bifurcation of limit cycles for a class of quintic Hamiltonian systems with quartic perturbed terms

运用判定函数方法,借助于数值计算方法研究了一类五次哈密顿系统在四次多项式扰动下的极限环分支情况,通过获得的判断曲线得出系统可以同时分支出6个极限环,而且6个极限环的情况有((3,0),3)和((0,3),3)两种分布形式.使用数值探测方法对所得结果进行了模拟检验,给出了6个极限环的具体位置.而且研究了该系统在一些特殊扰动下的极限环数目及分布情况.

By using the method of detection function and numerical calculation,the bifurcation of limit cycles for a class of quintic Hamiltonian systems under quartic perturbations was studied.Through the obtained detection curves,it is found that the system can branch out 6 limit cycles at the same time,and the case of 6 limit cycles has two distribution forms of((3,0),3)and((0,3),3).The results are verified by using the numerical detection method,and the specific positions of the 6 limit cycles are given.Moreover,the number and distribution of limit cycles of this system under some special disturbances are studied.