9个扰动哈密顿系统的极限环分布

 用微分方程定性分析方法和数值模拟方法研究9个扰动哈密顿系统的极限环个数和分布情况.结果显示9个系统具有相同的极限环分布,在某些参数条件下它们都有14个极限环.数值模拟给出了这14个极限环的精确位置.

The same distribution of limit cycles in nine perturbed Hamiltonian systems

Using the method of qualitative analysis it investigates the number and distribution of limit cycles for a cubic Hamiltonian system with nine different nine-order perturbed terms. It shows that these perturbed systems have the same distribution of limit cycles. Furthermore, these systems have 14 limit cycles for some parameters. The accurate location of each limit cycle is given by numerical exploration. Our results imply that these perturbed systems are equivalent in the sense of distribution of limit cycles. This is useful for studying limit cycles of perturbed systems.