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.