Safe and dangerous bifurcation points in non-autonomous dynamical systems

Dynamical systems described by periodic differential equations depending on a scalar parameter are considered. The types of bifurcation points (safe or dangerous) are determined and the behavior of the system when its parameters pass through the bifurcation point is studied. The basic formulas are obtained in terms of the initial equations and do not require a transition to normal forms and the use of theorems about the central manifold.