Mean First Passage Time in Periodic Attractors

Abstract

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: $T=\frac{c}{\tau }\exp (\frac{\tau }{\epsilon }\Delta \mathcal{U})$; the ratio between the sizes of the two attractors affects $\Delta \mathcal{U}$. 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.

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

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