Reconstruction of Integrate-and-fire Dynamics

The fact that the geometry of state space can be reconstructed from a time series of observations has led to innovative prediction and control algorithms for chaotic systems. In this article we show that state reconstruction of integrate-and-re dynamics is possible from a series of interspike intervals. In particular, a chaotic spike train generated in this way can be predicted from its history. We show that it is possible to use system reconstruction based on spike trains alone to control unstable periodic trajectories of the system in two separate ways: by making small (subthreshold) changes in a system parameter, and by using an on-demand pacing protocol with large (superthreshold) pulses.