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Publisher DOI: 10.3389/fams.2022.756699
Title: Classification of codimension-1 singular bifurcations in low-dimensional DAEs
Language: English
Authors: Ovsyannikov, Ivan 
Ruan, Haibo  
Keywords: bifurcation; differential algebraic equation (DAE); fold; singular induced bifurcation; slow-fast dynamics
Issue Date: 18-Mar-2022
Publisher: Frontiers Media
Source: Frontiers in Applied Mathematics and Statistics 8: 756699 (2022-03-18)
Abstract (english): 
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.
DOI: 10.15480/882.4322
ISSN: 2297-4687
Journal: Frontiers in applied mathematics and statistics 
Institute: Mathematik E-10 
Document Type: Article
Project: Oberflächenwellengetriebene Energieflüsse zwischen Ozean und Atmosphäre 
Funded by: Deutsche Forschungsgemeinschaft (DFG) 
More Funding information: The article is also supported by the grant of the Russian Science Foundation 19-11-00280.
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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