  Complex systems close to their critical state can exhibit abrupt transitions,
avalanches, between their metastable states. It is a challenging task to
understand the mechanism of the avalanches and control their behavior. Here we
investigate microwave (mw) stimulation of avalanches in the so- called vortex
matter of type II superconductors, a system of interacting Abrikosov vortices
close to the critical (Bean) state. Our main finding is that the avalanche
incubation strongly depends on the excitation frequency, a completely
unexpected behavior observed close to the so-called depinning frequencies.
Namely, the triggered vortex avalanches in Pb superconducting films become
effectively inhibited approaching the critical temperature or critical magnetic
field when the mw stimulus is close to the vortex depinning frequency. We
suggest a simple model explaining the observed counter- intuitive behaviors as
a manifestation of the strongly nonlinear dependence of the driven vortex core
size on the mw excitation intensity. This paves the way to controlling
avalanches in complex systems through their nonlinear response.
