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.
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References
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)
Horimoto, N., Saito, T.: Analysis of Digital Spike Maps based on Bifurcating Neurons. NOLTA, IEICE E95-N(10), 596–605 (2012)
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)
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)
Chua, L.O.: A nonlinear dynamics perspective of Wolfram’s new kind of science, I, II. World Scientific (2005)
Wada, W., Kuroiwa, J., Nara, S.: Completely reproducible description of digital sound data with cellular automata. Physics Letters A 306, 110–115 (2002)
Kouzuki, R., Saito, T.: Learning of simple dynamic binary neural networks. IEICE Trans. Fundamentals E96-A(8), 1775–1782 (2013)
Campbell, S.R., Wang, D., Jayaprakash, C.: Synchrony and desynchrony in integrate-and-fire oscillators. Neural Computation 11, 1595–1619 (1999)
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)
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)
Izhikevich, E.M.: Simple Model of Spiking Neurons. IEEE Trans. Neural Networks 14(6), 1569–1572 (2003)
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)
Amari, S.: A Method of Statistical Neurodynamics. Kybernetik 14, 201–215 (1974)
Perez, R., Glass, L.: Bistability, period doubling bifurcations and chaos in a periodically forced oscillator. Phys. Lett. 90A(9), 441–443 (1982)
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)
Ott, E.: Chaos in dynamical systems, Cambridge (1993)
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Yamaoka, H., Horimoto, N., Saito, T. (2014). Basic Feature Quantities of Digital Spike Maps. In: Wermter, S., et al. Artificial Neural Networks and Machine Learning – ICANN 2014. ICANN 2014. Lecture Notes in Computer Science, vol 8681. Springer, Cham. https://doi.org/10.1007/978-3-319-11179-7_10
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DOI: https://doi.org/10.1007/978-3-319-11179-7_10
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