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A digital implementation of 2D Hindmarsh–Rose neuron

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Abstract

Different architectures and techniques have developed in the neuromorphic field to mimic and investigate the activity of biological neural networks. This paper presents a set of piece-wise linear approximations of a two-dimensional Hindmarsh–Rose neuron model for digital circuit implementation to achieve higher speeds and lower hardware costs in large-scale implementation of the biological neural networks. The performance of the model was evaluated with a time domain signal error. Synthesis and hardware implementation on a field-programmable gate array, as a proof of concept, indicates that the proposed model reproduces several neuronal behaviors similar to the original model with higher performance and considerably lower implementation costs.

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References

  1. Bluebrain|EPFL (2016). http://bluebrain.epfl.ch

  2. Benjamin, B.V., Gao, P., McQuinn, E., Choudhary, S., Chandrasekaran, A.R., Bussat, J.M., Alvarez-Icaza, R., Arthur, J.V., Merolla, P.A., Boahen, K.: A mixed-analog-digital multichip system for large-scale neural simulations. Proc. IEEE 102(5), 699–716 (2014)

    Article  Google Scholar 

  3. Brette, R.: Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. J. Neurophysiol. 94(5), 3637–3642 (2005)

    Article  Google Scholar 

  4. Brink, S., Nease, S., Hasler, P., Ramakrishnan, S., Wunderlich, R., Basu, A., Degnan, B.: A learning-enabled neuron array IC based upon transistor channel models of biological phenomena. IEEE Trans. Biomed. Circuits Syst. 7(1), 71–81 (2013)

    Article  Google Scholar 

  5. Cognitive Computation Project (2016). http://ibm.com

  6. Cameron, S.H.: Piece-wise linear approximations. Technical Report CSTN-106, Computer Science Division , IIT Research Institute, Chicago, IL (1996)

  7. Cassidy, A.S., Georgiou, J., Andreou, A.G.: Design of silicon brains in the nano-cmos era: spiking neurons, learning synapses and neural architecture optimization. Neural Netw. 45, 4–26 (2013)

    Article  Google Scholar 

  8. Chen, S.S., Chrng, C.Y., Lin, Y.R.: Application of a two-dimensional hindmarsh-rose type model for bifurcation analysis. Int. J. Bifurc. Chaos 23(03), 1350,055 (2013)

    Article  MathSciNet  Google Scholar 

  9. Dahasert, N., Öztürk, İ., Kiliç, R.: Experimental realizations of the hr neuron model with programmable hardware and synchronization applications. Nonlinear Dyn. 70(4), 2343–2358 (2012)

    Article  MathSciNet  Google Scholar 

  10. FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445–466 (1961)

    Article  Google Scholar 

  11. Gallego, G., Berjon, D., Garcia, N.: Optimal polygonal \(l_{1}\) linearization and fast interpolation of nonlinear systems. IEEE Trans. Circuits Syst. I Regul. Papers 61(11), 3225–3234 (2014)

    Article  MathSciNet  Google Scholar 

  12. Ghosh-Dastidar, S., Adeli, H.: Spiking Neural Networks: Third Generation Neural Networks. Springer, Berlin (2009)

    Google Scholar 

  13. Gomar, S., Ahmadi, A.: Digital multiplierless implementation of biological adaptive-exponential neuron model. IEEE Trans. Circuits Syst. I Regul. Papers 61(4), 1206–1219 (2014)

    Article  Google Scholar 

  14. Grassia, F., Levi, T., Kohno, T., Saghi, S.: Silicon neuron: digital hardware implementation of the quartic model. Artif Life Robot. 19(3), 215–219 (2014)

    Article  Google Scholar 

  15. Hayati, M., Nouri, M., Abbott, D., Haghiri, S.: Digital multiplierless realization of two-coupled biological hindmarsh; rose neuron model. IEEE Trans. Circuits Syst. II Express Br. 63(5), 463–467 (2016)

    Article  Google Scholar 

  16. Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. Bull. Math. Biol. 52(1–2), 25–71 (1990)

    Article  Google Scholar 

  17. Indiveri, G., Linares-Barranco, B., Hamilton, T.J., van Schaik, A., Etienne-Cummings, R., Delbruck, T., Liu, S.C., Dudek, P., Hafliger, P., Renaud, S., Schemmel, J., Cauwenberghs, G., Arthur, J., Hynna, K., Folowosele, F., Saighi, S., Serrano-Gotarredona, T., Wijekoon, J., Wang, Y., Boahen, K.: Neuromorphic silicon neuron circuits. Front. Neurosci. 5, 73 (2011)

    Google Scholar 

  18. Izhikevich, E.: Simple model of spiking neurons. IEEE Trans. Neural Netw. 14(6), 1569–1572 (2003)

    Article  MathSciNet  Google Scholar 

  19. Izhikevich, E.M.: Which model to use for cortical spiking neurons? IEEE Trans. Neural Netw. 15(5), 1063–1070 (2004)

    Article  Google Scholar 

  20. Izhikevich, E.M.: Dynamical Systems in Neuroscience. MIT Press, Cambridge (2007)

    Google Scholar 

  21. Kazemi, A., Ahmad, A., Ahmad, S.: A digital synthesis of hindmarsh-rose neuron: a thalamic neuron model of the brain. In: 2014 22nd Iranian Conference on Electrical Engineering (ICEE), pp. 238–241 (2014)

  22. Kosslyn, S.M., Andersen, R.A.: Frontiers in Cognitive Neuroscience. MIT Press, Cambridge (1992)

    Google Scholar 

  23. Lee, Y.J., Lee, J., Kim, Y.B., Ayers, J., Volkovskii, A., Selverston, A., Abarbanel, H., Rabinovich, M.: Low power real time electronic neuron vlsi design using subthreshold technique. In: Proceedings of the 2004 International Symposium on Circuits and Systems, 2004. ISCAS ’04, vol. 4, pp. 744–747 (2004)

  24. Lv, M., Ma, J.: Multiple modes of electrical activities in a new neuron model under electromagnetic radiation. Neurocomputing 205, 375–381 (2016)

    Article  Google Scholar 

  25. Lv, M., Wang, C., Ren, G., Ma, J., Song, X.: Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn. 85(3), 1479–1490 (2016)

    Article  Google Scholar 

  26. Matsubara, T., Torikai, H., Hishiki, T.: A generalized rotate-and-fire digital spiking neuron model and its on-FPGA learning. IEEE Trans. Circuits and Syst. II Express Br. 58(10), 677–681 (2011)

    Article  Google Scholar 

  27. Morris, C., Lecar, H.: Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35(1), 193–213 (1981)

    Article  Google Scholar 

  28. Morrison, A., Diesmann, M., Gerstner, W.: Phenomenological models of synaptic plasticity based on spike timing. Biol. Cybern. 98(6), 459–478 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  29. Nemo (2016). http://nemosim.sourceforge.net/

  30. Nest Simulator|The Neural Simulation Tool (2016). http://www.nest-simulator.org/

  31. Neil, D., Liu, S.C.: Minitaur, an event-driven fpga-based spiking network accelerator. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 22(12), 2621–2628 (2014)

    Article  Google Scholar 

  32. Oliveri, A., Reimers, M., Storace, M.: Automatic domain partitioning of piecewise-affine simplicial functions implementing model predictive controllers. IEEE Trans. Circuits Syst. II Express Br. 62(9), 886–890 (2015)

    Article  Google Scholar 

  33. Poggi, T., Sciutto, A., Storace, M.: Piecewise linear implementation of nonlinear dynamical systems: from theory to practice. Electron. Lett. 45(19), 966–967 (2009)

    Article  Google Scholar 

  34. Ponulak, F., Kasinski, A.: Introduction to spiking neural networks: information processing, learning and applications. Acta Neurobiol. Exp. 71(4), 409–433 (2011)

    Google Scholar 

  35. Postnov, D., Ryazanova, L., Sosnovtseva, O.: Functional modeling of neural-glial interaction. Biosystems 89(1–3), 84–91 (2007)

    Article  Google Scholar 

  36. Radhika, E., Kumar, S., Kumari, A.: Low power analog VLSI implementation of cortical neuron with threshold modulation. In: 2015 International Conference on Advances in Computing, Communications and Informatics (ICACCI), pp. 561–566 (2015)

  37. Rose, R.M., Hindmarsh, J.L.: The assembly of ionic currents in a thalamic neuron I. The three-dimensional model. Proc. R. Soc. B Biol. Sci. 237(1288), 267–288 (1989)

    Article  Google Scholar 

  38. Sharifipoor, O., Ahmadi, A.: An analog implementation of biologically plausible neurons using CCII building blocks. Neural Netw. 36, 129–135 (2012)

    Article  Google Scholar 

  39. Soleimani, H., Ahmadi, A., Bavandpour, M.: Biologically inspired spiking neurons: piecewise linear models and digital implementation. IEEE Trans. Circuits and Syst. I Regul. Papers 59(12), 2991–3004 (2012)

    Article  MathSciNet  Google Scholar 

  40. Song, X., Wang, C., Ma, J., Tang, J.: Transition of electric activity of neurons induced by chemical and electric autapses. Sci. China Technol. Sci. 58(6), 1007–1014 (2015)

    Article  Google Scholar 

  41. Starzyk, J.A.: Basawaraj: memristor crossbar architecture for synchronous neural networks. IEEE Trans. Circuits Syst. I Regul. Papers 61(8), 2390–2401 (2014)

    Article  Google Scholar 

  42. Storace, M., Linaro, D., de Lange, E.: The Hindmarsh-Rose neuron model: bifurcation analysis and piecewise-linear approximations. Chaos 18(3), 033128 (2008)

    Article  MathSciNet  Google Scholar 

  43. The Brain Spiking Neural Network Simulator (2016). http://briansimulator.org/

  44. The Human Brain Project (2016). https://www.humanbrainproject.eu

  45. Tewari, S.G., Majumdar, K.K.: A mathematical model of the tripartite synapse: astrocyte-induced synaptic plasticity. J. Biol. Phys. 38(3), 465–496 (2012)

    Article  Google Scholar 

  46. Torikai, H.: Learning of digital spiking neuron and its application potentials. In: Applications of Nonlinear Dynamics: Model and Design of Complex Systems, pp. 273–285. Springer, Heidelberg (2009)

  47. Tsuji, S., Ueta, T., Kawakami, H., Fujii, H., Aihara, K.: Bifurcations in two-dimensional Hindmarsh–Rose type mode. Int. J. Bifurc. Chaos 17(03), 985–998 (2007)

    Article  MATH  Google Scholar 

  48. Wilson, H.R.: Simplified dynamics of human and mammalian neocortical neurons. J. Theor. Biol. 200(4), 375–388 (1999)

    Article  Google Scholar 

  49. Yamashita, Y., Torikai, H.: A novel PWC spiking neuron model: neuron-like bifurcation scenarios and responses. IEEE Trans. Circuits Syst. I Regul. Papers 59(11), 2678–2691 (2012)

    Article  MathSciNet  Google Scholar 

  50. Yildiz, N., Cesur, E., Kayaer, K., Tavsanoglu, V., Alpay, M.: Architecture of a fully pipelined real-time cellular neural network emulator. IEEE Trans. Circuits Syst. I Regul. Pap. 62(1), 130–138 (2015)

    Article  Google Scholar 

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Correspondence to Arash Ahmadi.

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Heidarpur, M., Ahmadi, A. & Kandalaft, N. A digital implementation of 2D Hindmarsh–Rose neuron. Nonlinear Dyn 89, 2259–2272 (2017). https://doi.org/10.1007/s11071-017-3584-0

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  • DOI: https://doi.org/10.1007/s11071-017-3584-0

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