Singularity induced bifurcations of dissipative MHD systems

We analyze the traveling wave solutions of dissipative MHD systems described by either nonlinear DAEs or singularly perturbed ODEs and their bifurcations at singularities. The typical behavior of nonlinear MHD DAEs follows from the Singularity Induced Bifurcation Theorem, while the behavior of the singularly perturbed MHD ODEs is described by the Singular Hopf Bifurcation Theorem. In spite of the obvious similarities, the MHD DAEs response is quite different than that of the singularly perturbed MHD ODEs. A few illustrative example are included.