New Solutions of Resistive MHD Systems With Singularity Induced Bifurcations

We show how the singularity induced bifurcation from differential algebraic equations can be applied to analyze certain resistive magneto-hydrodynamic (MHD) systems having supersonic to subsonic heteroclinic orbits transversally crossing the sonic (singularity) manifold. The connection is through an equilibrium point (either state 2 or state 3 in the MHD language) placed at the singularity manifold. The equilibrium status of state 2 (or 3) is lost and, at the same time, an impasse point is "killed" at the singularity manifold allowing a smooth trajectory to connect regular equilibria on the supersonic and subsonic sheets