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

Abstract

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 ̇ =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.