Bifurcations of MHD DAEs at singularities

We analyze the traveling wave differential-algebraic equations (DAEs) in magnetohydrodynamics (MHD) and their behavior at singularities. The parameter dependent MHD DAEs may, under certain conditions, undergo the singularity induced bifurcation (SIB) when one eigenvalue of the linear model diverges through infinity. This local phenomenon may in turn signal Hopf bifurcation in the respective singularly perturbed traveling wave MHD ODEs. The qualitative analysis is based on matrix pencils and parameter dependent polynomials. Several numerical examples are given.