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 1nW ∝(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.

Date Published: 7 May 2003
PDF: 10 pages
Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); doi: 10.1117/12.497700

Published in SPIE Proceedings Vol. 5114:
Noise in Complex Systems and Stochastic Dynamics
Lutz Schimansky-Geier; Derek Abbott; Alexander Neiman; Christian Van den Broeck, Editor(s)