Classification of parametrically constrained bifurcations
Classification of parametrically constrained bifurcations
复制标题
DOI：
10.1007/s10483-010-0201-z
复制
发表时间：
2010-02
影响因子：
--
通讯作者：
Zhiqiang Wu;R. Ding;Yushu Chen
中科院分区：
文献类型：
--
作者：
Zhiqiang Wu;R. Ding;Yushu Chen
如果约束边界与分叉参数有关，则称分叉为参数约束。借助于某种替换，将参数约束分歧转化为关于新变量的无约束分歧。导出了参数约束分岔的过渡集的一般形式。结果表明，只有约束分支集受参数约束的影响，而其他过渡集与相应的非参数约束分支的过渡集相同。以含参数约束的分叉问题为例，讨论了参数约束对分叉分类的影响。
If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unconstrained bifurcation about new variables. A general form of transition sets of the parametrically constrained bifurcation is derived. The result indicates that only the constrained bifurcation set is influenced by parametric constraints, while other transition sets are the same as those of the corresponding nonparametrically constrained bifurcation. Taking parametrically constrained pitchfork bifurcation problems as examples, effects of parametric constraints on bifurcation classification are discussed.