A singularity-induced bifurcation theorem for infinite-dimensional implicit dynamical systems (Q2748080)
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scientific article; zbMATH DE number 1658873
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A singularity-induced bifurcation theorem for infinite-dimensional implicit dynamical systems |
scientific article; zbMATH DE number 1658873 |
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14 October 2001
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implicit differential equations
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linear stability
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bifurcation
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A singularity-induced bifurcation theorem for infinite-dimensional implicit dynamical systems (English)
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A class of partial differential equations whose formal structure resembles the semiexplicit, index-1 form from DAEs is considered. It is known from the theory on such problems, that one can encounter simple poles in the eigenvalue loci of parameter-dependent linearizations, leading to a loss of linear stability without the presence of steady-state bifurcations. Here, it is demonstrated how this phenomenon can be carried over to implicit problems defined on a Hilbert space.
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