A novel hybrid spiking neuron: Bifurcations, responses, and on-chip learning

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 57, Issue 8, 2010, Pages 2168-2181

  Hashimoto, Sho ^a   Torikai, Hiroyuki ^a  

^a OSAKA UNIVERSITY   (Japan)

Author keywords

Bifurcation; discrete state dynamics; field programmable gate array (FPGA); forced oscillator; learning; spiking neuron model

Indexed keywords

BIFURCATION (MATHEMATICS); FIELD PROGRAMMABLE GATE ARRAYS (FPGA); LOGIC GATES; NEURONS; SHIFT REGISTERS;

BIFURCATION PHENOMENA; CONTINUOUS-DISCRETE; DISCRETE STATE; FORCED OSCILLATORS; LEARNING; ONLINE LEARNING ALGORITHMS; RESPONSE CHARACTERISTIC; SPIKING NEURON MODELS;

LEARNING ALGORITHMS;

EID: 77955663250     PISSN: 15498328     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2010.2041507     Document Type: Article

References (40)

1. E. M. Izhikevich, Dynamical Systems in Neuroscience. Cambridge, MA: MIT Press, 2006.
2. A. Hodgkin and A. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol., vol.117, no.4, pp. 500-544, Aug. 1952.
3. E. M. Izhikevich, "Simple model of spiking neurons," IEEE Trans. Neural Netw., vol.14, no.6, pp. 1569-1572, Nov. 2003.
4. E. M. Izhikevich, "Resonate-and-fire neurons," Neural Netw., vol.14, no.6, pp. 883-894, Jul. 2001.
5. E. M. Izhikevich, "Which model to use for cortical spiking neurons?," IEEE Trans. Neural Netw., vol.15, no.5, pp. 1063-1070, Sep. 2004.
6. K. Mitsubori and T. Saito, "Dependent switched capacitor chaos generator and its synchronization," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol.44, no.12, pp. 1122-1128, Dec. 1997.
7. H. Nakano and T. Saito, "Grouping synchronization in a pulse-coupled network of chaotic spiking oscillators," IEEE Trans. Neural Netw., vol.15, no.5, pp. 1018-1026, Sep. 2004.
8. R. Perez and L. Glass, "Bistability, period doubling bifurcations and chaos in a periodically forced oscillator," Phys. Lett. A, vol.90, no.9, pp. 441-443, Aug. 1982.
9. H. Hamanaka, H. Torikai, and T. Saito, "Quantized spiking neuron with A/D conversion functions," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.53, no.10, pp. 1049-1053, Oct. 2006.
10. H. Torikai and T. Saito, "Resonance phenomenon of interspike intervals from an integrate-and-fire model with two periodic inputs," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol.48, no.10, pp. 1198-1204, Oct. 2001.
11. H. Torikai, H. Hamanaka, and T. Saito, "Reconfigurable spiking neuron and its pulse-coupled networks: Basic characteristics and potential applications," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.53, no.8, pp. 734-738, Aug. 2006.
12. H. Torikai, A. Funew, and T. Saito, "Digital spiking neuron and its learning for approximation of various spike-trains," Neural Netw., vol. 21, no. 2/3, pp. 140-149, Mar./Apr. 2008.
13. H. Torikai and T. Nishigami, "An artificial chaotic spiking neuron inspired by spiral ganglion cell: Paralleled spike encoding, theoretical analysis, and electronic circuit implementation," Neural Netw., vol. 22, no. 5/6, pp. 664-673, Jul./Aug. 2009, accepted for publication.
14. H. Torikai, "Basic characteristics and learning potential of a digital spiking neuron," IEICE Trans. Fundam. Electron. Commun. Comput. Sci., vol.E90-A, no.10, pp. 2093-2100, Oct. 2007.
15. W. Maas and C. Bishop, Pulsed Neural Networks. Cambridge, MA: MIT Press, 2001.
16. W. Gerstner and W. Kistler, Spiking Neuron Models. Cambridge, U.K.: Cambridge Univ. Press, 2002.
17. R. Eckhorn, "Neural mechanisms of scene segmentation: Recordings from the visual cortex suggest basic circuits for linking field models," IEEE Trans. Neural Netw., vol.10, no.3, pp. 464-479, May 1999.
18. P. Checco, M. Righero, M. Biey, and L. Kocarev, "Synchronization in networks of Hindmarsh-Rose neurons," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.55, no.12, pp. 1274-1278, Dec. 2008.
19. S.Wolfram, "Universality and complexity in cellular automata," Phys. D, vol. 10, no. 1/2, pp. 1-35, Jan. 1984.
20. L. O. Chua, S. Yoon, and R. Dogaru, "A nonlinear dynamics perspective ofWolfram's newkind of science. Part I: Threshold of complexity," Int. J. Bifurc. Chaos, vol.12, no.12, pp. 2655-2766, 2002.
21. D. E. Knuth, The Art of Computer Programming, 3rd ed. Reading, MA: Addison-Wesley, 1998, vol.2.
22. L. Cheng, Z. Hou, and M. Tan, "A neutral-type delayed projection neural network for solving nonlinear variational inequalities," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.55, no.8, pp. 806-810, Aug. 2008.
23. W. Chen and W. Zheng, "Global exponential stability of impulsive neural networks with variable delay: An LMI approach," IEEE Trans. Circuits Syst. I, Reg. Papers, vol.56, no.6, pp. 1248-1259, Jun. 2009.
24. T. W. Berger, A. Ahuja, S. H. Courellis, S. A. Deadwyler, G. Erinjippurath, G. A. Gerhardt, G. Gholmieh, J.J. Granacki, R. Hampson, M. C. Hsiao, J. Lacoss, V. Z. Marmarelis, P. Nasiatka, V. Srinivasan, D. Song, A. R. Tanguay, and J. Wills, "Restoring lost cognitive function: Hippocampal-cortical neural prostheses," IEEE Eng. Med. Biol. Mag., vol.24, no.5, pp. 30-44, Sep./Oct. 2005.
25. , T. W. Berger and D. L. Glanzman, Eds., Toward Replacement Parts for the Brain: Implantable Biomimetic Electronics as Neural Prosthesis. Cambridge, MA: MIT Press, 2005.
26. S. Martignoli, J.-J. van der Vyver, A. Kern, Y. Uwate, and R. Stoop, "Analog electronic cochlea with mammalian hearing characteristics," Appl. Phys. Lett., vol.91, no.6, p. 064108, Aug. 2007.
27. C. D. Geisler, From Sound to Synapse: Physiology of the Mammalian Ear. Oxford, U.K.: Oxford Univ. Press, 1998.
28. [Online]. Available: http://www.neural-prosthesis.com/
29. G. Bi and M. Poo, "Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type," J. Neurosci., vol.18, no.24, pp. 10464-10472, Dec. 1998.
30. M. G. Benedetto and G. Giancola, Understanding Ultra Wide Band Radio Fundamentals. Englewood Cliffs, NJ: Prentice-Hall, 2004.
31. G. M. Maggio, N. Rulkov, and L. Reggiani, "Pseudo-chaotic time hopping for UWB impulse radio," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol.48, no.12, pp. 1424-1435, Dec. 2001. (Pubitemid 34055363)
32. A. Gerosa, S. Solda, A. Bevilacqua, D. Vogrig, and A. Neviani, "An energy-detector for noncoherent impulse-radio UWB receivers," IEEE Trans. Circuits Syst. I, Reg. Papers, vol.46, no.5, pp. 1030-1040, May 2009.
33. W. Chu and C. J. Colbourn, "Sequence designs for ultra-wideband impulse radio with optimal correlation properties," IEEE Trans. Inf. Theory, vol.50, no.10, pp. 2402-2407, Oct. 2004.
34. J. Gao and Y. Chang, "Newupper bounds for impulse radio sequences," IEEE Trans. Inf. Theory, vol.52, no.5, pp. 2255-2260, May 2006.
35. S. Hashimoto and H. Torikai, "A novel hybrid spiking neuron: Response analysis and learning potential," in Proc. Int. Conf. Neural Inf. Process., 2008, pp. 145-152.
36. S. Hashimoto and H. Torikai, "Bifurcation analysis of a reconfigurable hybrid spiking neuron and its novel online learning algorithm," in Proc. IEEE-INNS IJCNN, 2009, pp. 1134-1141.
37. S. Iplikci, "Dynamic reconstruction of chaotic systems from inter-spike intervals using least squares support vector machines," Phys. D, vol.216, no.2, pp. 282-293, Apr. 2006.
38. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed. Reading, MA: Addison-Wesley, 1995.
39. E. Ott, Chaos in Dynamical Systems. Cambridge, U.K.: Cambridge Univ. Press, 1993.
40. Z. Michalewicz and D. Fogel, How to Solve It: Modern Heuristics. Berlin, Germany: Springer-Verlag, 2000.