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.
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References
Horimoto, N., Saito, T.: Analysis of Digital Spike Maps based on Bifurcating Neurons. NOLTA, IEICE, E95-N 10, 596–605 (2012)
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)
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)
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)
Ott, E.: Chaos in dynamical systems. Cambridge (1993)
Campbell, S.R., Wang, D., Jayaprakash, C.: Synchrony and desynchrony in integrate-and-fire oscillators. Neural Computation 11, 1595–1619 (1999)
Izhikevich, E.M.: Simple Model of Spiking Neurons. IEEE Trans. Neural Networks 14(6), 1569–1572 (2003)
Torikai, H., Funew, A., Saito, T.: Digital spiking neuron and its learning for approximation of various spike-trains. Neural Networks 21, 140–149 (2008)
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)
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)
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)
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)
Torikai, H., Saito, T., Schwarz, W.: Synchronization via multiplex pulse-train. IEEE Trans. Circuits Syst. I 46(9), 1072–1085 (1999)
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Horimoto, N., Saito, T. (2013). Digital Dynamical Systems of Spike-Trains. In: Lee, M., Hirose, A., Hou, ZG., Kil, R.M. (eds) Neural Information Processing. ICONIP 2013. Lecture Notes in Computer Science, vol 8227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-42042-9_24
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DOI: https://doi.org/10.1007/978-3-642-42042-9_24
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