Classification of Codimension-1 Singular Bifurcations in Low-Dimensional DAEs

Ovsyannikov, Ivan and Ruan, Haibo (2022) Classification of Codimension-1 Singular Bifurcations in Low-Dimensional DAEs. Frontiers in Applied Mathematics and Statistics, 8. ISSN 2297-4687

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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.

Item Type: Article
Subjects: Eurolib Press > Mathematical Science
Depositing User: Managing Editor
Date Deposited: 29 Mar 2023 05:08
Last Modified: 07 May 2024 04:21

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