一类余维2系统的分支

LOCAL BIFURCATION OF A CODIMENSION-TWO SYSTEM

讨论了一类 4次多项式系统的分支问题 .采用简化分支问题的典型方法 ,用正规形理论和中心流形定理将系统简化 ,讨论系统的奇点分支、闭轨分支 ,给出了系统的所有局部分支曲线 ,得到参数平面上向量场的轨线分布图 .

This paper mainly discusses the bifurcation problem of a polynomial vector field of degree 4.We use normal form theory and center manifold theory to simplify the dynamical system and study the singular point bifurcation and periodic bifurcation.All the local bifurcation curves and the orbit structure diagram in the parameter plane are given.