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Basic Feature Quantities of Digital Spike Maps

  • Hiroki Yamaoka
  • Narutoshi Horimoto
  • Toshimichi Saito
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8681)

Abstract

The digital spike-phase map is a simple digital dynamical system that can generate various spike-trains. In order to approach systematic analysis of the steady and transient states, four basic feature quantities are presented. Using the quantities, we analyze an example based on the bifurcating neuron with triangular base signal and consider basic four cases of the spike-train dynamics.

Keywords

digital spike-trains spiking neurons dynamical systems 

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References

  1. 1.
    Horimoto, N., Ogawa, T., Saito, T.: Basic Analysis of Digital Spike Maps. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds.) ICANN 2012, Part I. LNCS, vol. 7552, pp. 161–168. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Horimoto, N., Saito, T.: Analysis of Digital Spike Maps based on Bifurcating Neurons. NOLTA, IEICE E95-N(10), 596–605 (2012)Google Scholar
  3. 3.
    Horimoto, N., Saito, T.: Analysis of various transient phenomena and co-existing periodic spike-trains in simple digital spike maps. In: Proc. IJCNN, pp. 1751–1758 (2013)Google Scholar
  4. 4.
    Horimoto, N., Saito, T.: Digital Dynamical Systems of Spike-Trains. In: Lee, M., Hirose, A., Hou, Z.-G., Kil, R.M. (eds.) ICONIP 2013, Part II. LNCS, vol. 8227, pp. 188–195. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Chua, L.O.: A nonlinear dynamics perspective of Wolfram’s new kind of science, I, II. World Scientific (2005)Google Scholar
  6. 6.
    Wada, W., Kuroiwa, J., Nara, S.: Completely reproducible description of digital sound data with cellular automata. Physics Letters A 306, 110–115 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Kouzuki, R., Saito, T.: Learning of simple dynamic binary neural networks. IEICE Trans. Fundamentals E96-A(8), 1775–1782 (2013)Google Scholar
  8. 8.
    Campbell, S.R., Wang, D., Jayaprakash, C.: Synchrony and desynchrony in integrate-and-fire oscillators. Neural Computation 11, 1595–1619 (1999)CrossRefGoogle Scholar
  9. 9.
    Rulkov, N.F., Sushchik, M.M., Tsimring, L.S., Volkovskii, A.R.: Digital communication using chaotic-pulse-position modulation. IEEE Trans. Circuits Systs. I 48(12), 1436–1444 (2001)CrossRefGoogle 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.
    Izhikevich, E.M.: Simple Model of Spiking Neurons. IEEE Trans. Neural Networks 14(6), 1569–1572 (2003)MathSciNetGoogle Scholar
  12. 12.
    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
  13. 13.
    Amari, S.: A Method of Statistical Neurodynamics. Kybernetik 14, 201–215 (1974)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Perez, R., Glass, L.: Bistability, period doubling bifurcations and chaos in a periodically forced oscillator. Phys. Lett. 90A(9), 441–443 (1982)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Kirikawa, S., Ogawa, T., Saito, T.: Bifurcating Neurons with Filtered Base Signals. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds.) ICANN 2012, Part I. LNCS, vol. 7552, pp. 153–160. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  16. 16.
    Ott, E.: Chaos in dynamical systems, Cambridge (1993)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

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

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