Characterization of low-dimensional dynamics in the crayfish caudal photoreceptor

Abstract

ATTEMPTS to detect and characterize chaos in biological systems are of considerable interest, especially in medical science, where successful demonstrations may lead to new diagnostic tools and therapies¹. Unfortunately, conventional methods for identifying chaos often yield equivocal results when applied to biological data^2–8, which are usually heavily contaminated with noise. For such applications, a new technique¹ based on the detection of unstable periodic orbits holds promise. Infinite sets of unstable periodic orbits underlie chaos in dissipative systems^4,9; accordingly, the new method searches a time series only for rare events⁸ characteristic of these unstable orbits¹⁰, rather than analysing the structure of the series as a whole. Here we demonstrate the efficacy of the method when applied to the dynamics of the crayfish caudal photoreceptor (subject to stimuli representative of the animal's natural habitat). Our findings confirm the existence of low-dimensional dynamics in the system, and strongly suggest the existence of deterministic chaos. More importantly, these results demonstrate the power of methods based on the detection of unstable periodic orbits for identifying low-dimensional dynamics—and, in particular, chaos—in biological systems.