Persistence of the saddle-node bifurcation for nonlinear systems with slow unmodeled dynamics (Q1312202)

The authors study the persistence of a generic saddle-node bifurcation under the addition of slowly varying state variables (so-called ``unmodeled dynamics''). It is well-known that the saddle-node is robust under the addition of supplementary parameters (not varying in time). The paper gives (rather restrictive) conditions on the unmodeled dynamics which also imply the persistence of a saddle-node bifurcation under slowly varying perturbations. Several examples are given, in particular one involving a tree-bus power system consisting of a load supplied by two generators.