Characterizing chaotic dynamics from integrate-and-fire interspike intervals at the presence of noise

We discuss the problem of quantifying chaotic dynamics at the input of the "integrate-and-fire" (IF) model from the output sequences of interspike intervals (ISIs) for the case when the fluctuating threshold level leads to the appearance of noise in ISI series. We propose a way to detect an ability of computing dynamical characteristics of the input dynamics and the level of noise in the output point processes. The proposed approach is based on the dependence of the largest Lyapunov exponent from the maximal orientation error used at the estimation of the averaged rate of divergence of nearby phase trajectories.