Singularity Induced Bifurcation in Differential Algebraic Equations (with applications to magnetohydrodynamics)

Dr. Wieslaw Marszalek

Department of Mathematics
North Carolina State University

March 12, 1997

Abstract

We analyze parameter dependent differential algebraic equations, or DAEs, of the form

where p stands for parameters. Typically such DAEs have singularities if g_v = 0. We shall discuss a special type of bifurcation that may occur in such systems when an equilibrium point is moved to the singularity. In particular, the Singularity Induced Bifurcation Theorem will be presented and an outline of its proof will be discussed. Ana application of the theorem to the traveling wave DAEs in magnetohydrodynamics (MHD) will be given in some detail. Two numerical examples of MHD systems with various viscous coefficients are used to illustrate these results.