arXiv subjects
Publications and source records attributed to Daniel T. Kaplan.
Analysis of the PPF chaos control method used in biological experiments shows that it can robustly control a wider class of systems than previously believed, including those without stable manifolds. This can be exploited to find the locations of unstable periodic orbits by varying the parameters of the control system.
Dynamical control of excitable biological systems is often complicated by the difficult and unreliable task of pre-control identification of unstable periodic orbits (UPOs). Here we show that, for both chaotic and nonchaotic systems, UPOs 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 excitable biological systems, for which pre-control UPO identification is often impractical and nonstationarities (natural or stimulation-induced) are common.