Critical exponent crossovers in escape near a bifurcation point.

In periodically driven systems, near a bifurcation (critical) point the period-averaged escape rate $\overline{W}$ scales with the field amplitude $A$ as $|\mathrm{ln}\overline{W}|\ensuremath{\propto}({A}_{c}\ensuremath{-}A{)}^{\ensuremath{\xi}}$, where ${A}_{c}$ is a critical amplitude. We find three scaling regions. With increasing field frequency or decreasing $|{A}_{c}\ensuremath{-}A|$, the critical exponent $\ensuremath{\xi}$ changes from $\ensuremath{\xi}=3/2$ for a stationary system to a dynamical value $\ensuremath{\xi}=2$ and then again to $\ensuremath{\xi}=3/2$. Monte Carlo simulations agree with the scaling theory.