Bifurcation analysis of a degenerate vector field with non-symmetric terms

摘要：

The dynamics of a class of non-symmetric degenerate vector field are investigated. By analyzing the zeros of Melnikov function, we study Hopf and homoclinic bifurcations and their stability. Furthermore, using Picard-Fuchs equations we prove that double limit cycle bifurcations occur between the degenerate Hopf and homoclinic bifurcation points, moreover, the formula for calculating the bifurcation value of double limit cycle is derived. Finally, the complete bifurcation diagrams and associate phase portraits are obtained.

关键词： degenerate vector field bifurcation bifurcation diagrams non-symmetric

作者: Li Fan Jiping Chen

作者单位: Department of Automatic Control, Northwest Polytechnical University, Xian 710069 College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062

会议类型: 国际会议

会议名称: The 5th International Congress on Mathematical Biology(第五届国际生物数学大会 ICMB 2011)

会议地点: 南京

会议语种:英文

页码: 61-66

在线出版日期: 2011-06-01（万方平台首次上网日期，不代表论文的发表时间）