论文标题
在低维DAE中的Codimension-1奇异分叉的分类
Classification of Codimension-1 Singular Bifurcations in Low-dimensional DAEs
论文作者
论文摘要
差异化晶格方程（DAE）分叉的研究是许多应用科学的关注主题，例如电气工程，机器人技术等。尽管已经研究了其中一些科学，但尚未完成此类分叉的完整分类。在本文中，我们考虑了具有奇异性的准线性DAE的分叉，并在较低维度的情况下提供了所有consimension-One分叉的完整列表。除其他外，它包括奇异性引起的分叉（SIB），当平衡分支与奇异的歧管相交，导致线性化问题的某些特征值以偏离无穷大时，就会发生这种情况。对于这些和其他分叉，我们构建正常形式，建立非分类条件，并对动态进行定性描述。另外，我们研究了以前未考虑的奇异同型和杂斜分叉。
The study of bifurcations of differential-algebraic equations (DAEs) is the topic of interest for many applied sciences, such as electrical engineering, robotics, etc. While some of them were investigated already, the full classification of such bifurcations has not been done yet. In this paper, we consider bifurcations of quasilinear DAEs with a singularity and provide a full list of all codimension-one bifurcations in lower-dimensional cases. Among others, it includes singularity-induced bifurcations (SIBs), which occur when an equilibrium branch intersects a singular manifold causing certain eigenvalues of the linearized problem to diverge to infinity. For these and other bifurcations, we construct the normal forms, establish the non-degeneracy conditions and give a qualitative description of the dynamics. Also, we study singular homoclinic and heteroclinic bifurcations, which were not considered before.
