Detecting low dimensional dynamics in biological experiments

We discuss the well-known problems associated with efforts to detect and characterize chaos and other low dimensional dynamics in biological settings. We propose a new method which shows promise for addressing these problems, and we demonstrate its effectiveness in an experiment with the crayfish sensory system. Recordings of action potentials in this system are the data. We begin with a pair of assumptions: that the times of firings of neural action potentials are largely determined by high dimensional random processes or ''noise''; and that most biological files are non stationary, so that only relatively short files can be obtained under approximately constant conditions. The method is thus statistical in nature. It is designed to recognize individual ''events'' in the form of particular sequences of time intervals between action potentials which are the signatures of certain well defined dynamical behaviors. We show that chaos can be distinguished from limit cycles, even when the dynamics is heavily contaminated with noise. Extracellular recordings from the crayfish caudal photoreceptor, obtained while hydrodynamically stimulating the array of hair receptors on the tailfan, are used to illustrate the method.