  Parametric oscillators are examples of externally driven systems that can
exhibit two stable states with opposite phase depending on the initial
conditions. In this work, we propose to study what happens when the external
forcing is perturbed by a continuously parametrized defect. Initially in one of
its stable state, the oscillator will be perturbed by the defect and finally
reach another stable state, which can be its initial one or the other one. For
some critical value of the defect parameter, the final state changes abruptly.
We investigate theoretically and experimentally such transition both in the
linear and non-linear case, and the effect of non-linearities is discussed. A
topological interpretation in terms of winding number is proposed, and we show
that winding changes correspond to singularities in the temporal dynamics. An
experimental observation of such transition is performed using parametric
Faraday instability at the surface of a vibrated fluid.
