Advertisement

Digital Dynamical Systems of Spike-Trains

  • Narutoshi Horimoto
  • Toshimichi Saito
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8227)

Abstract

This paper studies a simple digital dynamical system that can generate various spike-trains. In order to consider the steady and transient states, we use two basic feature quantities. The first one is the number of co-existing periodic spike-trains that can characterize richness of the steady state. The second one is the concentricity of transition to the periodic spike-trains that can characterize variation of transient phenomena. Performing numerical experiments for two typical examples based on the bifurcating neuron, basic classification of the dynamics is considered.

Keywords

spiking neurons digital dynamical systems spike-train stability nonlinear dynamics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Horimoto, N., Saito, T.: Analysis of Digital Spike Maps based on Bifurcating Neurons. NOLTA, IEICE, E95-N 10, 596–605 (2012)CrossRefGoogle Scholar
  2. 2.
    Ogawa, T., Saito, T.: Self-organizing Digital Spike Interval Maps. In: Lu, B.-L., Zhang, L., Kwok, J. (eds.) ICONIP 2011, Part II. LNCS, vol. 7063, pp. 612–617. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Chua, L. O.: A nonlinear dynamics perspective of Wolfram’s new kind of science, I, II. World Scientific (2005)Google Scholar
  4. 4.
    Wada, W., Kuroiwa, J., Nara, S.: Completely reproducible description of digital sound data with cellular automata. Physics Letters A 306, 110-115 (2002)Google Scholar
  5. 5.
    Ito, R., Nakayama, Y., Saito, T.: Learning of Dynamic BNN toward Storing-and-Stabilizing Periodic Patterns. In: Lu, B.-L., Zhang, L., Kwok, J. (eds.) ICONIP 2011, Part II. LNCS, vol. 7063, pp. 606–611. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Ott, E.: Chaos in dynamical systems. Cambridge (1993)Google Scholar
  7. 7.
    Campbell, S.R., Wang, D., Jayaprakash, C.: Synchrony and desynchrony in integrate-and-fire oscillators. Neural Computation 11, 1595–1619 (1999)CrossRefGoogle Scholar
  8. 8.
    Izhikevich, E.M.: Simple Model of Spiking Neurons. IEEE Trans. Neural Networks 14(6), 1569–1572 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Torikai, H., Funew, A., Saito, T.: Digital spiking neuron and its learning for approximation of various spike-trains. Neural Networks 21, 140–149 (2008)CrossRefzbMATHGoogle Scholar
  10. 10.
    Torikai, H., Nishigami, T.: An artificial chaotic spiking neuron inspired by spiral ganglion cell: parallel spike encoding, theoretical analysis, and electronic circuit implementation. Neural Networks 22, 664–673 (2009)CrossRefGoogle Scholar
  11. 11.
    Rulkov, N.F., Sushchik, M.M., Tsimring, L.S., Volkovskii, A.R.: Digital communication using chaotic-pulse-position modulation. IEEE Trans. Circuits Systs., 48(12), 1436–1444 (2001)CrossRefGoogle Scholar
  12. 12.
    Iguchi, T., Hirata, A., Torikai, H.: Theoretical and heuristic synthesis of digital spiking neurons for spike-pattern-division multiplexing. IEICE Trans. Fundamentals, E93-A 8, 1486–1496 (2010)CrossRefGoogle Scholar
  13. 13.
    Matsubara, T., Torikai, H.: Asynchronous cellular automaton-based neuron: theoretical analysis and on-FPGA learning. IEEE Trans. Neiral Netw. Learning Systs. 24, 736–748 (2013)CrossRefGoogle Scholar
  14. 14.
    Amari, S.: A Method of Statistical Neurodynamics. Kybernetik 14, 201–215 (1974)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Perez, R., Glass, L.: Bistability, period doubling bifurcations and chaos in a periodically forced oscillator. Phys. Lett., 90A 9, 441–443 (1982)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Torikai, H., Saito, T., Schwarz, W.: Synchronization via multiplex pulse-train. IEEE Trans. Circuits Syst. I 46(9), 1072–1085 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Narutoshi Horimoto
    • 1
  • Toshimichi Saito
    • 1
  1. 1.Hosei UniversityKoganeiJapan

Personalised recommendations