高维映射的局部余维二分岔(Ⅰ)

Codimension Two Local Bifurcation of High Dimensional Map(Ⅰ)

应用中心流形 范式方法分析了高维映射在一实特征值和一对复共轭特征值同时穿越单位圆周情况下的余维二分岔 ,讨论了范式在余维二分岔点附近的局部分岔行为 .在余维二分岔点附近存在周期一点和周期二点的Hopf分岔 ,同时还存在倍周期分岔 ,但是由于周期二不动点类型的变化及周期二点的Hopf分岔 。

Codimension two bifurcation of high dimensional ma ps , undering the condition of a real eigenvalue and a pair of complex conjugate ei genvalues escaping the unit circle simultaneously, is analyzed by using the cent er manifold-normal form method of maps. Local bifurcation behavior of normal fo rm near by the point of codimension two bifurcation is discussed. It is shown t hat near by the point of codimension two bifurcation there exists not only Hopf bifurcation of period one, but also Hopf bifurcation of period two. Period doubl ing bifurcation exists simultaneously near by the point of codimension two bifur cation, however no period doubling cascade emerges due to the change of the type of period two fixed points and occurrence of Hopf bifurcation associated with p eriod two fixed points.