Mean first passage time in periodic attractors

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 neighbouring 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 ; the ratio between the sizes of the two attractors affects . 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.