Bifurcations of global reinjection orbits near a saddle-node Hopf bifurcation

The saddle-node Hopf bifurcation (SNH) is a generic codimension-two bifurcation of equilibria of vector fields in dimension at least three. It has been identified as an organizing centre in numerous vector field models arising in applications. We consider here the case that there is a global reinjection mechanism, because the centre manifold of the zero eigenvalue returns to a neighbourhood of the equilibrium. Such a SNH bifurcation with global reinjection occurs naturally in applications, most notably in models of semiconductor lasers.