Ovsyannikov, IvanIvanOvsyannikovRuan, HaiboHaiboRuan2022-05-032022-05-032022-03-18Frontiers in Applied Mathematics and Statistics 8: 756699 (2022-03-18)http://hdl.handle.net/11420/12417The 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.en2297-46872022Frontiers Mediahttps://creativecommons.org/licenses/by/4.0/bifurcationdifferential algebraic equation (DAE)foldsingular induced bifurcationslow-fast dynamicsMathematikJournal Article10.15480/882.432210.3389/fams.2022.75669910.15480/882.4322Journal Article