Interspike interval embedding of chaotic signals

According to a theorem of Takens [Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1981), Vol. 898], dynamical state information can be reproduced from a time series of amplitude measurements. In this paper we investigate whether the same information can be reproduced from interspike interval (ISI) measurements. Assuming an integrate-and-fire model coupling the dynamical system to the spike train, there is a one-to-one correspondence between the system states and interspike interval vectors of sufficiently large dimension. The correspondence implies in particular that a data series of interspike intervals, formed in this manner, can be forecast from past history. This capability is demonstrated using a nonlinear prediction algorithm, and is found to be robust to noise. A set of interspike intervals measured from a simple neuronal circuit is studied for deterministic structure using a prediction error statistic. (c) 1995 American Institute of Physics.