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

Mark I. Dykman; Brage Golding; Dmitrii Ryvkine

doi:10.1117/12.497700

7 May 2003 Critical exponents for escape of a strongly driven particle near a bifurcation point

Mark I. Dykman, Brage Golding, Dmitrii Ryvkine

Proceedings Volume 5114, Noise in Complex Systems and Stochastic Dynamics; (2003) https://doi.org/10.1117/12.497700
Event: SPIE's First International Symposium on Fluctuations and Noise, 2003, Santa Fe, New Mexico, United States

Abstract

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.

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Mark I. Dykman, Brage Golding, and Dmitrii Ryvkine "Critical exponents for escape of a strongly driven particle near a bifurcation point", Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); https://doi.org/10.1117/12.497700

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