Periodic solutions of daes with applications to dissipative electric circuits
MIC'06 Proceedings of the 25th IASTED international conference on Modeling, indentification, and control
Mixed-mode oscillations and chaotic solutions of jerk (Newtonian) equations
Journal of Computational and Applied Mathematics
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We extend the differential-algebraic equation (DAE) taxonomy by assuming that the linearization of a DAE about a singular equilibrium has a particular index-2 Kronecker normal form. A Lyapunov--Schmidt procedure is used to reduce the DAE to a quasilinear normal form which is shown to posses quasi-invariant manifolds which intersect the singularity. In turn, this provides solutions of the DAE which pass through the singularity.