The Same Distribution of Limit Cycles in a Hamiltonian System with Nine Seven-order Perturbed Terms  

作　　者：Tao Jiang Zhi-yan Yang 

机构地区：[1]School of Information, Beijing Wuzi University, Beijing, 101149, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第1期167-176,共10页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China (No. 10671063)

摘　　要：Using qualitative analysis and numerical simulation, we investigate the number and distribution of limit cycles for a cubic Hamiltonian system with nine different seven-order perturbed terms. It is showed that these perturbed systems have the same distribution of limit cycles. Furthermore, these systems have 13, 11 and 9 limit cycles for some parameters, respectively. The accurate positions of the 13, 11 and 9 limit cycles are obtained by numerical exploration, respectively. 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.Using qualitative analysis and numerical simulation, we investigate the number and distribution of limit cycles for a cubic Hamiltonian system with nine different seven-order perturbed terms. It is showed that these perturbed systems have the same distribution of limit cycles. Furthermore, these systems have 13, 11 and 9 limit cycles for some parameters, respectively. The accurate positions of the 13, 11 and 9 limit cycles are obtained by numerical exploration, respectively. 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.

关 键 词：Limit cycles BIFURCATION 

分 类 号：O153.3[理学—数学]