Advertisement

Artificial Life and Robotics

, Volume 7, Issue 3, pp 136–144 | Cite as

Symbolic dynamics of a chaotic neuron model

Original Article
  • 51 Downloads

Abstract

Chaotic neurons change their internal state according to a bimodal map, and when they communicate with other neurons their internal state is transformed into one of two separate outputs, firing or resting. We address and investigate the topological entropy of the two-valued output of the chaotic neuron from two different viewpoints: the dependence upon the parameters of the neurons, and the relationship to their threshold. From the former viewpoint, we clarify the mechanism that changes the shift space corresponding to the time series of the neuronal output. From the latter viewpoint, we examine the effect of small fluctuations on the threshold of the chaotic neuron.

Key words

Chaotic neuron Symbolic dynamics Fator code Parry measure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aihara K, Takabe T, Toyoda M (1990) Chaotic neural networks. Phys Lett A 144:333–340MathSciNetCrossRefGoogle Scholar
  2. 2.
    Adach M, Aihara K (1997) Associative dynamics in chaotic neural network. Neural Networks 10:83–98CrossRefGoogle Scholar
  3. 3.
    Bollt EM, Stanford T, Lai Y-C, et al. (2001) What symbolic dynamics do we get with a misplaced partition? On the validity of threshold crossings analysis of chaotic time-series. Physica D 154:259–286MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Crochemore M, Mignosi F, Restivo A (1998) Automata and forbidden words. Info Proc Lett 67:111–117MathSciNetCrossRefGoogle Scholar
  5. 5.
    Peng S-L, Zhang X-S (2000) The generalized Milnor-Thurston conjecture and equal topological entropy class in symbolic dynamics of order topological space of three letters. Commun Math Phys 213:381–411MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Katok A, Hasselblatt B (1995) Introduction to the modern theory of dynamic systems. Cambridge University Press, CambridgeGoogle Scholar
  7. 7.
    Buljan H, Paar V (2002) Parry measure and the topological entropy of chaotic repellers embedded within chaotic attractors. Physica D 1172:111–123MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hao B-L, Zheng W-M (1998) Applied symbolic dynamics and chaos. World ScientificGoogle Scholar
  9. 9.
    Fukuda K, Aihara K (2002) Symbolic dynamics of bimodal maps and regular languages. IEICE J85-A:930–937Google Scholar
  10. 10.
    Lind D, Marcus B (1995) An introduction to symbolic dynamics and coding. Cambridge University Press, New YorkMATHGoogle Scholar

Copyright information

© ISAROB 2003

Authors and Affiliations

  1. 1.Complexity Science and EngineeringUniversity of TokyoTokyoJapan
  2. 2.CRESTJapan Science and Technology CorporationSaitamaJapan

Personalised recommendations