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, $τ$, the noise, $ε$, and the potential difference between the attractor and an adjacent saddle point as: $~T = {c \over τ} \exp({τ\over ε} Δ{\cal{U}})~$; the ratio between the sizes of the two attractors affects $Δ{\cal{U}}$. The result is obtained analytically for small $τ$ and confirmed by numerical simulations. Possible implications that may arise from the model and results are discussed.