A Theory for Imperfect Bifurcation via Singularity Theory.
A Theory for Imperfect Bifurcation via Singularity Theory.
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DOI：
10.1002/cpa.3160320103
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发表时间：
1979
影响因子：
3
通讯作者：
M. Golubitsky;D. Schaeffer
中科院分区：
文献类型：
--
作者：
M. Golubitsky;D. Schaeffer
摘要：本文应用可微映射的奇点理论（特别是展开定理）来研究分岔系统中缺陷的影响。在许多特殊情况下，我们通过有限数量的缺陷参数对分岔方程的所有可能扰动进行了分类（直到合适的等价性）。这些情况包括来自双特征值的分岔和来自 Crandall-Rabinowitz 意义上的简单特征值退化的分岔。
Abstract : This paper applies the theory of singularities of differentiable mappings - specifically the unfolding theorem - to study the effect of imperfections in a system subject to bifurcation. In a number of special cases we have classified (up to a suitable equivalence) all the possible perturbations of the bifurcation equations by a finite number of imperfection parameters. These cases include both bifurcation from a double eigenvalue and from a simple eigenvalue degenerate in the sense of Crandall-Rabinowitz.