Scaling and crossovers in activated escape near a bifurcation point.

Near a bifurcation point a system experiences a critical slowdown. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node bifurcation where a metastable state disappears. The rate of activated escape W scales with the driving field amplitude A as ln W proportional, variant ( A(c) -A)(xi), where A(c) is the bifurcational value of A. With increasing field frequency the critical exponent xi changes from xi=3/2 for stationary systems to a dynamical value xi=2 and then again to xi=3/2. The analytical results are in agreement with the results of asymptotic calculations in the scaling region. Numerical calculations and simulations for a model system support the theory.