Mean First Passage Time in Periodic Attractors

Details Mean First Passage Time in Periodic Attractors Mean First Passage Time in Periodic Attractors

2006-03-16

arxiv.org/abs/math-ph/0603042v1

J. Phys. A: Math. Gen. 39 (2006) 8603-8612

Physics

Mathematical Physics

14 pages, 3 figures, submitted to journal of physics A

Scientific paper

10.1088/0305-4470/39/27/004

The properties of the mean first passage time in a system characterized by multiple periodic attractors are studied. Using a transformation from a high dimensional space to 1D, the problem is reduced to a stochastic process along the path from the fixed point attractor to a saddle point located between two neighboring attractors. It is found that the time to switch between attractors depends on the effective size of the attractors, $\tau$, the noise, $\epsilon$, and the potential difference between the attractor and an adjacent saddle point as: $~T = {c \over \tau} \exp({\tau \over \epsilon} \Delta {\cal{U}})~$; the ratio between the sizes of the two attractors affects $\Delta {\cal{U}}$. The result is obtained analytically for small $\tau$ and confirmed by numerical simulations. Possible implications that may arise from the model and results are discussed.

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