title: Scaling and crossovers in activated escape near a bifurcation point.
abstract: 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.
authors.affiliation: Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA.
authors.forename: D
authors.initials: D
authors.lastname: Ryvkine
authors.forename: M I
authors.initials: MI
authors.lastname: Dykman
authors.forename: B
authors.initials: B
authors.lastname: Golding