  We describe a new mechanism that triggers periodic orbits in smooth dynamical
systems. To this end, we introduce the concept of hybrid bifurcations: Such
bifurcations occur when a line of equilibria with an exchange point of normal
stability vanishes. Our main result is the existence and stability criteria of
periodic orbits that bifurcate from breaking a line of equilibria. As an
application, we obtain stable periodic coexistent solutions in an ecosystem for
two competing predators with Holling's type II functional response.

Dynamical Systems;Classical Analysis and ODEs