A Hopf bifurcation theorem for singular differential–algebraic equations
We prove a Hopf bifurcation result for singular differential–algebraic equations (DAE) under the assumption that a trivial locus of equilibria is situated on the singularity as the bifurcation occurs. The structure that we need to obtain this result is that the linearisation of the DAE has a particular index-2 Kronecker normal form, which is said to be simple index-2. This is so-named because the nilpotent mapping used to define the Kronecker index of the pencil has the smallest possible non-trivial rank, namely one. This allows us to recast the equation in terms of a singular normal form to which a local centre-manifold reduction and, subsequently, the Hopf bifurcation theorem applies.
Year of publication: |
2008
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Authors: | Beardmore, R. ; Webster, K. |
Published in: |
Mathematics and Computers in Simulation (MATCOM). - Elsevier, ISSN 0378-4754. - Vol. 79.2008, 4, p. 1383-1395
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Publisher: |
Elsevier |
Subject: | Hopf bifurcation | Singularity | Differential–algebraic equations |
Saved in:
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