Computation of the singularity induced bifurcation points in DAEs via extended system reduction

Singularity-induced bifurcation (SIB) with one parameter is considered. This kind of bifurcation arise in parameter dependent differential-algebraic equations (DAEs) of the form <(x)over dot> = f, 0 = g. The extended system reduction is introduced as a convenient method to compute the SIB points. Non-degeneracy conditions on the functions f and g are derived. Then under verification of these conditions, SIB points are associated with the non-degenerate equilibrium points of the extended system. An iterative method (e.g., Newton-Raphson) then can be used to compute the non-degenerate equilibrium points of the extended system which including the SIB points of the original DAEs. An example is given to illustrate the idea of this paper. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.