Communications in Mathematical Sciences

Volume 5 (2007)

Number 2

Self-induced stochastic resonance for Brownian ratchets under load

Pages: 431 – 466



R. E. Lee DeVille

Eric Vanden-Eijnden


We consider a Brownian ratchet model where the particle on the ratchet is coupled to a cargo. We show that in a distinguished limit where the diffusion coefficient of the cargo is small, and the amplitude of thermal fluctuations is small, the system becomes completely coherent: the times at which the particle jumps across the teeth of the ratchet become deterministic. We also show that the dynamics of the ratchet-cargo system do not depend on the fine structure of the Brownian ratchet. These results are relevant in the context of molecular motors transporting a load, which are often modeled as a ratchet-cargo compound. They explain the regularity of the motor gait that has been observed in numerical experiments, as well as justify the coarsening into Markov jump processes which is commonly done in the literature.


stochastic resonance; self-induced stochastic resonance; Brownian ratchets; molecular motors

2010 Mathematics Subject Classification

34E13, 60F10, 60G35, 60H10, 92C10

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