  We identify two rather novel types of (compound) dynamical bifurcations
generated primarily by interactions of an invariant attracting submanifold with
stable and unstable manifolds of hyperbolic fixed points. These bifurcation
types - inspired by recent investigations of mathematical models for walking
droplet (pilot-wave) phenomena - are introduced and illustrated. Some of the
one-parameter bifurcation types are analyzed in detail and extended from the
plane to higher-dimensional spaces. A few applications to walking droplet
dynamics are analyzed.
