Abstract: A new nonlinear dynamical analysis is applied to complex behavior from neuronal systems. The conceptual foundation of this analysis is the abstraction of observed neuronal activities into a dynamical landscape characterized by a hierarchy of "unstable periodic orbits" (UPOs). UPOs are rigorously identified in data sets representative Of three different levels of organization in mammalian brain. An analysis based on UPOs affords a novel altermative method of decoding, periodicting, and controlling these neur...