一类扰动五次哈密顿系统的极限环分支

Bifurcation of Limit Cycles for a Class of Quintic Hamiltonian Systems with Perturb Terms

运用判定函数方法,借助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分支出4个极限环,而且4个极限环的情况有((2,0),2)和((0,2),2)二种分布形式.使用数值探测方法对所得结果进行了模拟检验,并且给出了4个极限环的具体位置.

In this paper,the bifurcation of limit cycles for a class of quintic Hamiltonian systems with quartic polynomial perturbation is studied by using the method of detection function and numerical calculation.Through the obtained detection curves,it is found that the system can branch out into 4 limit cycles,and the case of 4 limit cycles has two distribution forms of((2,0),2)and((0,2),2).The results are verified by using the numerical detection method,and the specific positions of the 4 limit cycles are given.