Complex bifurcations in a periodically forced normal form

The effect of a periodic forcing on the normal form of a two-dimensional dynamical system, in which both roots of the characteristic equation can vanish simultaneously, is analyzed. In the space spanned by the system's parameters, the onset of nonperiodic behavior and subharmonic behavior are determined analytically using standard perturbation theory. Moreover it is shown that complex behavior can already appear in the immediate vicinity of singular points. An example of physico-chemical system amenable to the normal form is also constructed.