Skip to main content
Log in

On information-processing abilities of chaotic dynamical systems

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

A mechanism is suggested to explain the information processing abilities of simple natural brains, which, by experimental evidence, display behavior like chaotic dynamical systems while at rest. The Lorenz system of equations is dealt with as a case study, and a comparison of the suggested mechanism with the standard theory of neural networks is made.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D. J. Amit and A. Treves,J. Phys. A 22:2205 (1989).

    Google Scholar 

  2. H. L. Atwood and F. W. Tse, Changes in binormial parameters of quantal release at crustacean motor axon terminals during presynaptic inhibition,J. Physiol. (Lond.)402:177–193.

  3. A. Babloyantz and A. Destexhe, The Creutzfeldt-Jakob disease in the hierarchy of chaotic attractors, inFrom Chemical to Biological Organization M. Marcus, S. Muller, and S. Nicolis, eds. (Springer-Verlag, Berlin, 1988), pp. 307–316.

    Google Scholar 

  4. S. L. Bressler, The gamma wave: A cortical information carrier?,TINS 13:161–162 (1990).

    Google Scholar 

  5. J. Buhmann, Oscillations and low firing rates in associative memory neural networks,Phys. Rev. A 40(7):4145–4148 (1989).

    Google Scholar 

  6. L. Cesari,Asymptotic Behavior and Stability Problems in Ordinary Differential Equations (Springer-Verlag, Berlin, 1963).

    Google Scholar 

  7. J. D. Clements, I. D. Forsythe, and S. J. Redman, Presynaptic inhibition of synaptic potentials evoked in cat spinal motoneurons by impulses in single group Ia axons,J. Physiol. (Lond.)388:153–169 (1987).

    Google Scholar 

  8. J. Dudel and S. W. Kuffler, Presynaptic inhibition at the crayfish neuromuscular junction,J. Physiol. 155:543–562 (1961).

    Google Scholar 

  9. J. C. Eccles,The Physiology of Synapses (Springer-Verlag, Berlin, 1964).

    Google Scholar 

  10. C. M. Gray and W. Singer, Stimulus specific neuronal oscillations in orientation columns of cat visual cortex,Proc. Natl. Acad. Sci. USA 86:1698–1702 (1989).

    Google Scholar 

  11. C. M. Gray, P. Konig, A. K. Engel, and W. Singer, Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties,Nature 338:384–337 (1989).

    Google Scholar 

  12. J. Guckenheimer and P. Holmes,Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, Berlin, 1986).

    Google Scholar 

  13. J. J. Hopfield, Neurons with graded response have collective computational properties like those of two state neurons,Proc. Natl. Acad. Sci. USA 81:3088–3092 (1984).

    Google Scholar 

  14. H. C. Kwan, T. H. Yeap, B. C. Jiang, and L. Borrett, Neural network control of simple limb movements,Can. J. Physiol Pharmacol. 68:126–130 (1990).

    Google Scholar 

  15. O. E. Lanford, Qualitative and statistical theory of dissipative systems, University of California at Berkeley, preprint (1976).

  16. E. Lorentz, Deterministic nonperiodic flow,J. Atmos. Sci. 20:130–141 (1963).

    Google Scholar 

  17. G. Mayer-Kress, F. E. Yates, L. Benton, M. Keidel, W. Tirsch, J. Poppl, and K. Geist, Dimension analysis of nonlinear oscillations in brain, heart and muscle,Math. Biosci. 90:155–182 (1988).

    Google Scholar 

  18. G. J. Mpitsos, R. M. Burton, H. C. Creech, and S. O. Soinila, Evidence for chaos in spike trains of neurons that generate rhythmic motor patterns,Brain Res. Bull. 21:529–538 (1988).

    Google Scholar 

  19. G. Parisi, Asymmetric neural networks and the process of learning,J. Phys. A: Math. Gen. 19:L675-L680 (1986).

    Google Scholar 

  20. B. A. Pearlmutter, Learning state space trajectories in recurrent neural networks, inIEEE International Joint Conference on Neural Networks, Vol. 2, pp. II-365–372.

  21. F. Pineda, Generalization of back-propagation to recurrent neural networks,Phys. Rev. Lett. 19:2229–2232 (1987).

    Google Scholar 

  22. P. E. Rapp, I. D. Zimmerman, A. M. Albano, G. C. de Guzman, N. N. Greenbaum, and T. R. Bashore, Experimental studies of chaotic neural behavior: Cellular activity and electroencephalographic signals, inNonlinear Oscillations in Biology and Chemistry, H. G. Othmer, ed. (Springer-Verlag, New York, 1985), pp. 175–205.

    Google Scholar 

  23. A. Skarda and W. J. Freeman, How brains make chaos in order to make sense of the world,Behav. Brain Sci. 10:161–195 (1987).

    Google Scholar 

  24. C. Sparrow,The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. (Springer-Verlag, Berlin, 1982).

    Google Scholar 

  25. A. C. K. Soong and C. I. J. M. Stuart, Evidence of chaotic dynamics underlying the human alpha-rhythm electroencephalogram,Biol. Cybernet. 62:55–62 (1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Evans, N.W., Illner, R. & Kwan, H.C. On information-processing abilities of chaotic dynamical systems. J Stat Phys 66, 549–561 (1992). https://doi.org/10.1007/BF01060080

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01060080

Key words

Navigation