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Scaling and crossovers in activated escape near a bifurcation point

D. Ryvkine·M. I. Dykman·B. Golding
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Abstract

Near a bifurcation point a system experiences critical slowing down. 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 $\ln W \propto (A_c-A)^ξ$, where $A_c$ is the bifurcational value of $A$. With increasing field frequency the critical exponent $ξ$ changes from $ξ= 3/2$ for stationary systems to a dynamical value $ξ=2$ and then again to $ξ=3/2$. 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.

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D. Ryvkine, M. I. Dykman, B. Golding. 2003-12-05. Scaling and crossovers in activated escape near a bifurcation point. https://doi.org/10.1103/physreve.69.061102

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