Shift of attractor boundaries in a system with a slow harmonic parameter perturbation

In a dynamical system with coexisting attractors, a slow periodic modulation of a control parameter deforms attractor boundaries by shifting saddle-node and inverse period-doubling bifurcation points. Dynamical properties of these points are studied numerically and experimentally in a loss-driven CO2 laser with additional slow modulation of the cavity losses. Shifted positions of the bifurcation points depend on the amplitude and frequency of the control modulation. The new position of the saddle-node bifurcation point obeys a particular scaling law for small modulation frequencies and amplitudes.