Critical exponents for escape of a strongly driven particle near a bifurcation point

We study the rate of activated escape W in periodically modulated systems close to the saddle-node bifurcation point where the metastable state disappears. The escape rate displays scaling behavior versus modulation amplitude A as A approaches the bifurcational value A c , with 1n W ∝( A c - A )μ. For adiabatic modulation, the critical exponent is μ=3/2. Even if the modulation is slow far from the bifurcation point, the adiabatic approximation breaks down close to A c . In the weakly nonadiabatic regime we predict a crossover to μ = 2 scaling. For higher driving frequencies, as A c is approached there occurs another crossover, from Αμ=2 to μ=3/2. The general results are illustrated using a simple model system.