Using the method of multi-parameter perturbation theory and qualitative analysis,a cubic system perturbed by degree four are investigated in this paper. After systematic analysis,it is found that the studied system ca...Using the method of multi-parameter perturbation theory and qualitative analysis,a cubic system perturbed by degree four are investigated in this paper. After systematic analysis,it is found that the studied system can have nine limit cycles with their distributions are obtained.展开更多
This paper concerns the number and distributions of limit cycles in a Z 2-equivariant quintic planar vector field. 25 limit cycles are found in this special planar polynomial system and four different configurations o...This paper concerns the number and distributions of limit cycles in a Z 2-equivariant quintic planar vector field. 25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation. It can be concluded that H(5) ? 25 = 52, where H(5) is the Hilbert number for quintic polynomial systems. The results obtained are useful to study the weakened 16th Hilbert problem.展开更多
In this paper, we employ qualitative analysis and methods of bifurcation theory to study the maximum number of limit cycles for a polynomial system with center in global bifurcation.
基金supported by the Natural Science Foundation of Shandong Province,China（No.ZR2010AZ003）
文摘Using the method of multi-parameter perturbation theory and qualitative analysis,a cubic system perturbed by degree four are investigated in this paper. After systematic analysis,it is found that the studied system can have nine limit cycles with their distributions are obtained.
基金the Natural Science Foundation of Anhui Province(1308085MA08)the Doctor Program Foundation(2012)of Anhui Normal University+1 种基金the NNSF of China(11271197)the key NSF of Education Ministry of China(207047)
基金Supported by the Fund of Youth of Jiangsu University(Grant No.05JDG011)the National Natural Science Foundation of China(Nos.90610031,10671127)+1 种基金the Outstanding Personnel Program in Six Fields of Jiangsu Province(Grant No.6-A-029)Shanghai Shuguang Genzong Project(Grant No.04SGG05)
文摘This paper concerns the number and distributions of limit cycles in a Z 2-equivariant quintic planar vector field. 25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation. It can be concluded that H(5) ? 25 = 52, where H(5) is the Hilbert number for quintic polynomial systems. The results obtained are useful to study the weakened 16th Hilbert problem.
基金supported by Foundation of Shanghai Municipal Education Committee (10YZ72)
文摘In this paper, we employ qualitative analysis and methods of bifurcation theory to study the maximum number of limit cycles for a polynomial system with center in global bifurcation.
