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Classification of codimension-1 singular bifurcations in low-dimensional DAEs
Citation Link: https://doi.org/10.15480/882.4322
Publikationstyp
Journal Article
Date Issued
2022-03-18
Sprache
English
Author(s)
Institut
TORE-DOI
Volume
8
Article Number
756699
Citation
Frontiers in Applied Mathematics and Statistics 8: 756699 (2022-03-18)
Publisher DOI
Scopus ID
Publisher
Frontiers Media
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.
Subjects
bifurcation
differential algebraic equation (DAE)
fold
singular induced bifurcation
slow-fast dynamics
DDC Class
510: Mathematik
Funding Organisations
More Funding Information
The article is also supported by the grant of the Russian Science Foundation 19-11-00280.
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