Correlation dimension of attractors through interspike intervals

The question whether the correlation dimension of an experimental chaotic dynamical system can be determined from a series of spike timings produced by the system is considered. Two separate, biologically motivated methods for generating spikes from the system are surveyed: an integrate-and-fire model and a threshold-crossing method. Computational evidence indicates that the dimension can be determined in principle under either method, assuming that the embedding dimension of the interspike interval attractor reconstruction is greater than or equal to the correlation dimension of the attractor. The dependence of the dimension statistics on the threshold level and the amount of available data is investigated.