高维映射的局部余维二分岔(Ⅱ)

Codimension Two Local Bifurcation of High Dimensional Map (Ⅱ)

应用中心流形 范式方法分析了高维映射在两个实特征值同时穿越单位圆周情况下的余维二分岔 .根据中心流形定理 ,高维映射与被降维的简化映射的局部分岔行为是等价的 .通过分析范式在余维二分岔点附近的局部分岔行为 ,可以了解映射f(v,X)

Codimension two bifurcation of high dimensional map is analyzed by center manifo ld theory and normal form method under the situation that two real eigenvalues e scape unit circle simultaneously.According to center manifold theory, high dimen sional map and simplified map are equivalent near by bifurcation point. The loca l bifurcation characteristic near by codimension two bifurcation point is discus sed,which testifies that the local dynamical behavior of map f(v ,X)may be known under the condition of codimension two bifurcation.