Abstract
This paper studies digital spike maps that can generate various periodic spike-trains. In order to analyze the maps, we present a simple analysis algorithm to calculate basic feature quantities. We then analyze a typical example of the map given by discretizing the bifurcating neuron. Applying the algorithm to the example, we demonstrate complex dynamics and give basic classification of the dynamics.
This work is supported in part by JSPS KAKENHI#24500284.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Lee, G., Farhat, N.H.: The bifurcating neuron network 1. Neural Networks 14, 115–131 (2001)
Chua, L.O.: A nonlinear dynamics perspective of Wolfram’s new kind of science, I, II. World Scientific (2005)
Rosin, P.L.: Training Cellular Automata for Image Processing. IEEE Trans. Image Process. 15(7), 2076–2087 (2006)
Wada, W., Kuroiwa, J., Nara, S.: Completely reproducible description of digital sound data with cellular automata. Physics Letters A 306, 110–115 (2002)
Ott, E.: Chaos in dynamical systems, Cambridge (1993)
Izhikevich, E.M.: Simple Model of Spiking Neurons. IEEE Trans. Neural Networks 14(6), 1569–1572 (2003)
Campbell, S.R., Wang, D., Jayaprakash, C.: Synchrony and desynchrony in integrate-and-fire oscillators. Neural Computation 11, 1595–1619 (1999)
Sushchik, M., Rulkov, N., Larson, L., Tsimring, L., Abarbanel, H., Yao, K., Volkovskii, A.: Chaotic pulse position modulation: a robust method of communicating with chaos. IEEE Comm. Lett. 4, 128–130 (2000)
Torikai, T., 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)
Torikai, H., Saito, T.: Analysis of a quantized chaotic system. Int’l J. of Bifurcation and Chaos 12(5), 1207–1218 (2002)
Torikai, H., Funew, A., Saito, T.: Digital spiking neuron and its learning for approximation of various spike-trains. Neural Networks 21, 140–149 (2008)
Ogawa, T., Saito, T.: Digital spike maps and learning of spike signals. In: Proc. IEEE-INNS Int’l. Joint Conf. Neural Netw, pp. 1587–1592 (2010)
Ogawa, T., Saito, T.: Self-organizing Digital Spike Maps for Learning of Spike-Trains. IEICE Trans. Fundamentals E94-A(12), 2845–2852 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Horimoto, N., Ogawa, T., Saito, T. (2012). Basic Analysis of Digital Spike Maps. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds) Artificial Neural Networks and Machine Learning – ICANN 2012. ICANN 2012. Lecture Notes in Computer Science, vol 7552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33269-2_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-33269-2_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33268-5
Online ISBN: 978-3-642-33269-2
eBook Packages: Computer ScienceComputer Science (R0)