Interspike interval attractors from chaotically driven neuron models

Sequences of intervals between firing times (interspike intervals (ISIs)) from single neuron models with chaotic forcing are investigated. We analyze how the dynamical properties of the chaotic input determine those of the output ISI sequence, and assess how various biophysical parameters affect this input-output relationship. The attractors constructed from delay embeddings of ISIs and of the chaotic input are compared from the points of view of geometry and nonlinear forecastability. For the three integrate-and-fire (IF) models investigated, the similarity between these attractors is high only when the mean firing rate is high, and when firings occur over a large range of the input signal. When these conditions are satisfied, ISIs are related to input values at which firings occur by a simple map, and their distribution can be derived from that of input signal values. Attractor reconstruction is found to be more sensitive to mean firing rate than to ISI distribution. At low firing rates, for which the input is under sampled and ISIs become larger than the short-term prediction horizon, or when the dynamics do not allow a smooth invertible mapping between signal and ISIs, information is lost. Our results, relevant to all dynamical systems generating events, show that information about continuous-time dynamics is difficult to retrieve at low event rates, and that information about inputs can be isolated only under restricted conditions.