一类扰动七次哈密顿系统的极限环

Limit Cycles for a Class of Perturbed Seventh Order Hamiltonian Systems

研究了一类带有幂零奇点的七次超椭圆哈密顿系统在特殊七次多项式扰动下的极限环情况.应用判定函数和数值模拟方法得出该系统在无界环域中有3个极限环,而且模拟出了这些极限环的具体位置.

The limit cycles of a class of seventh order hyperelliptic Hamiltonian systems with nilpotent singular points under the perturbation of seventh degree polynomial are studied to find that the system has three limit cycles in the unbounded ring domain,and the specific positions of these limit cycles are simulated by using the detection function and numerical simulation method.