Adaptive estimation and control method for unstable periodic dynamics in spike trains

Dynamical control of excitable biological systems is often complicated by the difficult and unreliable task of precontrol identification of unstable periodic orbits (UPO’s). Here we show that, for both chaotic and nonchaotic systems, UPO’s can be located, and their dynamics characterized, during control. Tracking of system nonstationarities emerges naturally from this approach. Such a method is potentially valuable for the control of spike trains of excitable biological systems, for which precontrol UPO identification is often impractical, and nonstationarities (natural or stimulation induced) are common.