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, ǫ, and the potential difference between the attractor and an adjacent saddle point as: T = c τ exp( τ ǫ ∆U) ; the ratio between the sizes of the two attractors affects ∆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.