Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:D3L-B

Session:

Number:899

A Simple Chaotic Circuit Based on Coupled Spiking Neurons

Shinya Tanaka,  Toshimichi Saito,  Kunihiko Mitsubori,  

pp.899-902

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.899

PDF download (415.7KB)

Summary:
This paper studies chaotic spiking oscillators with two integrate-and-fire switches. The circuit has signum activation function and piecewise constant vector field that is well suited for precise analysis. The two firing switches can cause interesting chaotic behavior that is hard in the case of one firing switch. Using the piecewise linear return map, the dynamics can be analyzed precisely. Presenting a simple test circuit, typical phenomena are confirmed in laboratory.

References:

[1] J. P. Keener, F. C. Hoppensteadt and J.∼Rinzel, “Integrate-and-fire models of nerve membrane response to oscillatory input”, SIAM J. Appl. Math., 41, pp. 503-517, 1981.

[2] R. Perez and L. Glass, “Bistability, period doubling bifurcations and chaos in a periodically forced oscillator”, Phys. Lett., 90A, 9, pp. 441-443, 1982.

[3] R. E. Mirollo and S. H. Strogatz, “Synchronization of pulse-coupled biological oscillators”, SIAM J. Appl. Math., 50, 6, pp.1645-1662, 1990.

[4] E. M. Izhikevich, “Resonate-and-fire neurons”, Neural Networks, 14, pp. 883-894, 2001.

[5] E. M. Izhikevich, “Simple Model of Spiking Neurons”, IEEE Trans. Neural Networks, 14, pp. 1569-1572, 2003.

[6] Y. Yamashita and H. Torikai, Bursting Analysis and Synapse Mechanism of A Piece-wise Constant Spiking Neuron Model, Proc. IJCNN, pp. 193-200, 2012.

[7] T. Toyoizumi, K. Aihara and S. Amari, “Fisher information for spikebased population coding”, Phys. Rev. Lett., 97, 098102, 2006.

[8] S. R. Campbell, D. Wang and C. Jayaprakash, “Synchrony and desynchrony in integrate-and-fire oscillators”, Neural computation, vol. 11, pp. 1595-1619, 1999.

[9] G. M. Maggio, N. Rulkov and L. Reggiani, “Pseudo-Chaotic Time Hopping For UWB Impulse Radio”, IEEE Tran. Circuits Syst., I, 48, 12, pp. 1424-1435, 2001.

[10] S. Hashimoto and H. Torikai, “A Novel Hybrid Spiking Neuron: Bifurcations, Responses, and On-Chip Learning”, IEEE Trans. Circuits Syst. I, 57, 8, pp. 2168-2181, 2010.

[11] K. Mitsubori and T. Saito, “Dependent switched capacitor chaos generator and its synchronization”, IEEE Trans. Circuits Syst. I, 44, 12, pp. 1122-1128, 1997.

[12] K. Mitsubori and T. Saito, “Mutually Pulse-coupled Chaotic Circuits by using Dependent Switched Capacitors, IEEE Trans. Circuits Syst. I, 47, 10, pp. 1469-1478, 2000.

[13] H. Nakano and T. Saito, “Basic dynamics from a pulse-coupled network of autonomous integrate-and-fire chaotic circuits”, IEEE Trans. Neural Networks, 13, 1, pp. 92-100, 2002.

[14] Y. Takahashi, H. Nakano and T. Saito, “A simple hyperchaos generator based on impulsive switching”, IEEE Trans. Circuits Syst. II, 51, 9, pp. 468-472, 2004.

[15] H. Nakano and T. Saito, “Grouping synchronization in a pulse-coupled network of chaotic spiking oscillators”, IEEE Trans. Neural Networks, 15, 5, pp. 1018-1026, 2004.

[16] Y. Matsuoka and T. Saito, “A Simple Chaotic Spiking Oscillator Having Piecewise Constant Characteristics”, IEICE Trans. Fundamentals, 89, 9, pp. 2437-2440, 2006.

[17] Y. Matsuoka, T. Hasegawa and T. Saito, “Chaotic Spike-train with Line-like Spectrum”, IEICE Trans. Fundamentals, E92-A, 4, pp. 1142-1147, 2009.

[18] T. Tsubone and T. Saito, “Manifold piecewise constant systems and chaos”, IEICE Trans. Fundamentals, E82-A, 8, pp.1619-1626, 1999.