ISSN:
1531-5878
Keywords:
Linearly implicit differential equations
;
semiexplicit differential-algebraic equations
;
singular equilibria
;
weak singularities
;
nonlinear electrical circuits
;
singular flow
;
singularity induced bifurcation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract Some qualitative properties of singular equilibria arising in semiexplicit index-1 differential-algebraic equations are discussed in this paper. We extend a taxonomy of singularities from index-0 problems to address situations not covered by the singularity induced bifurcation, singular flow, and associated theorems. Although some related phenomena may occur, different behavior can be expected when the assumptions supporting these results are not satisfied, as is illustrated by several examples. Special attention is paid to the effect that the singular nature of the underlying ordinary differential equation and, eventually, of the solution manifold, has on the behavior of the original singular index-1 problem.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01212467
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