A generically singular type of saddle–node bifurcation that occurs for relativistic shock waves

Abstract

This paper is concerned with two-parameter families of planar dynamical systems in which a saddle–node bifurcation interacts with a singular perturbation. We identify bifurcation curves along which the non-saddle point switches from node to focus and establish the existence of heteroclinic connections in either case. As an application, the result is used to show the existence of oscillatory shock profiles in a model of relativistic fluid dynamics.