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 data2–8, 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 systems4,9; 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.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Schiff, S. J. et al. Nature 370, 615–620 (1994).
Ruelle, D. Physics Today 47, 24–30 (1994).
Ruelle, D. Proc. R. Soc. Lond. A 427, 241–251 (1990).
Cvitanovic, P. Physica D51, 138–156 (1991).
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. & Farmer, J. D. Physica D58, 77–94 (1992).
Chang, T., Schiff, S. J., Sauer, T., Gossard, J-P. & Burke, R. E. Biophys. J. 67, 671–683 (1994).
Scott, D. A. & Schiff, S. J. Biophys. J. 69, 1748–1757 (1995).
Kaplan, D. Physica D73, 38–48 (1994).
Cvitanovic, P. Phys. Rev. Lett. 61, 2729–2732 (1988).
Pierson, D. & Moss, F. Phys. Rev. Lett. 75, 2124–2127 (1995).
Ruelle, D. & Takens, F. Commun math. Phys. 20, 167–192 (1971).
Ruelle, D. La Richerche 108, 132–246 (1980).
Ruelle, D. in 8th Int. Congress on Math. Phys. (eds Mebkhout, M. & Senior, R.) 273–282 (World Scientific, Singapore, 1987).
May, R. M. Nature 261, 459–467 (1976).
May, R. M. Ann. N.Y. Acad. Sci. 316, 517–529 (1979).
Proc. 2nd Workshop on Measures of Complexity and Chaos (eds Abraham, N. B., Albano, A. M., Passamante, A. P., Rapp, P. E. & Gilmore, R.) Int. J. Bifurc. Chaos 3, 485–490 (1993).
Grassberger, P. & Procaccia, I. Physica D9, 189–208 (1983).
Wolf, A., Swift, J. B., Swinney, H. L. & Vasano, J. A. Physica D16, 285–317 (1985).
Sugihara, G. & May, R. M. Nature 344, 734–741 (1990).
Garfinkel, A., Spano, M. L., Ditto, W. L. & Weiss, J. N. Science 257, 1230–1235 (1992).
Christini, D. J. & Collins, J. J. Phys. Rev. Lett. 75, 2782–2785 (1995).
Kennedy, D. J. gen. Physiol. 46, 551–572 (1963).
Wilkens, L. A. Comp. Biochem. Physiol. 91, 61–68 (1988).
Wilkens, L. A. & Douglass, J. K. J. exp. Biol. 189, 263–272 (1994).
Hayashi, H. & Ishizuka, A. J. theor. Biol. 156, 269–291 (1992).
Bevington, P. R. Data Reduction and Error Analysis 48–49 (McGraw-Hill, New York, 1969).
Ditto, W. L., Rauseo, S. N. & Spano, M. L. Phys. Rev. Lett. 65, 3211–3214 (1990).
Hunt, E. R. Phys. Rev. Lett. 67, 1953–1955 (1991).
Roy, R., Murphy, T. W., Maier, T. D. & Gills, Z. Phys. Rev. Lett. 68, 1259–1262 (1992).
Petrov, V., Gaspar, V., Masere, J. & Showalter, K. Nature 361, 240–243 (1993).
Rollins, R. W., Parmananda, P. & Sherard, P. Phys. Rev. E47, R780–R784 (1993).
Artuso, R., Aurell, E. & Cvitanovic, P. Nonlinearity 3, 325–360 (1990).
Artuso, R., Aurell, E. & Cvitanovic, P. Nonlinearity 3, 361–395 (1990).
Shinbrot, R., Grebogi, C., Ott, E. & Yorke, J. A. Nature 363, 411–417 (1993).
Moon, F. C. Chaotic Vibrations (Wiley, New York, 1987).
Strogatz, S. H. Nonlinear Dynamics and Chaos Ch. 12 (Addison-Wesley. Reading, 1994).
Herman, H. T. & Olsen, R. E. J. gen Physiol. 51, 534–551 (1968).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pei, X., Moss, F. Characterization of low-dimensional dynamics in the crayfish caudal photoreceptor. Nature 379, 618–621 (1996). https://doi.org/10.1038/379618a0
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/379618a0
This article is cited by
-
Fractional-Order Periodic Maps: Stability Analysis and Application to the Periodic-2 Limit Cycles in the Nonlinear Systems
Journal of Nonlinear Science (2023)
-
Capturing the continuous complexity of behaviour in Caenorhabditis elegans
Nature Physics (2021)
-
Variability of bursting patterns in a neuron model in the presence of noise
Journal of Computational Neuroscience (2009)
-
Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis
Acta Mechanica Sinica (2008)