access icon free 0.65 V integrable electronic realisation of integer- and fractional-order Hindmarsh–Rose neuron model using companding technique

© The Institution of Engineering and Technology
Received 18/03/2018, Accepted 08/08/2018, Revised 10/07/2018, Published 13/08/2018

Some neurons like neocortical pyramidal neurons adapt with multiple time-scales, which is consistent with fractional-order differentiation. The fractional-order neuron models are therefore believed to portray the firing rate of neurons more accurately than their integer-order models. It has been studied that as the fractional order of differentiator and integrator involved in the neuron model decreases, bursting frequency of the neurons increases. The opposite effect has been observed on increasing the external excitation. In this study, integer- and fractional-order Hindmarsh–Rose (HR) neuron models have been implemented using sinh companding technique. Besides, the application of the HR neuron model in a simple network of two neurons has also been considered. The designs offer a low-voltage and low-power implementation along with the electronic tunability of the performance characteristics. Due to the use of only metal-oxide semiconductor (MOS) transistors and grounded capacitors, the proposed implementation can be integrated in chip form. On comparing with existing implementations, the implemented fractional-order and integer-order models show a better performance in terms of power consumption, supply voltage, order and flexibility. The performance of the circuits has been verified using 130 nm complementary MOS (CMOS) technology process provided by Austrian Micro Systems using HSPICE simulation software.

Inspec keywords: integrated circuit design; integrated circuit modelling; CMOS integrated circuits; synchronisation; low-power electronics; neural chips; MOSFET circuits

Other keywords: MOS transistors; neocortical pyramidal neurons; HR neuron models; complementary metal–oxide–semiconductor technology process; voltage 0.65 V; HSPICE simulation software; integer-order models; integrator; sinh companding technique; HR neuron model; electronic tunability; fractional-order differentiation; differentiator; grounded capacitors; fractional-order Hindmarsh–Rose neuron model; firing rate; multiple time-scales; size 130.0 nm; integrable electronic realisation; external excitation

Subjects: CMOS integrated circuits; Semiconductor integrated circuit design, layout, modelling and testing; Neural nets (circuit implementations)

References

    1. 1)
      • 28. Hong, J.Y., Hua, J.P.: ‘Chaotic control of the Hindmarsh–Rose model’, Acta Biophys. Sin., 2005, 21, (4), pp. 295–300.
    2. 2)
      • 18. Diamantopoulos, C., Psychalinos, C.: ‘Mihalas–Niebuhr model implementation using Sinh-Domain integrators’, Analog Integr. Circuits Signal Process., 2016, 88, (1), pp. 161–171.
    3. 3)
      • 24. Kazemi, A., Ahmadi, A., Gomar, S.: ‘A digital synthesis of Hindmarsh- Rose neuron: a thalamic neuron model of the brain’. Proc. of 22nd Iranian Conf. on Electrical Engineering (ICEE), Tehran, Iran, 2014, pp. 238–241.
    4. 4)
      • 11. Kaslik, E., Sivasundaram, S.: ‘Nonlinear dynamics and chaos in fractional-order neural networks’, Neural Netw., 2012, 32, pp. 245–256.
    5. 5)
      • 6. Magin, R.L.: ‘Fractional calculus models of complex dynamics in biological tissues’, Comput. Math. Appl., 2010, 59, pp. 1586–1593.
    6. 6)
      • 35. Deng, W., Li, C., Lu, J.: ‘Stability analysis of linear fractional differential system with multiple time delays’, Nonlinear Dyn., 2007, 48, (4), pp. 409–416.
    7. 7)
      • 30. Wei, D.Q., Luo, X.S.: ‘Coherence resonance and noise-induced synchronization in Hindmarsh–Rose neural network with different topologies’, Commun. Theor. Phys., 2007, 48, (4), pp. 759–762.
    8. 8)
      • 4. Jun, D., Jun, Z.G., Yong, X., et al: ‘Dynamic behaviour analysis of fractional-order Hindmarsh–Rose neuronal model’, Cogn. Neurodynamics, 2014, 8, (2), pp. 167–175.
    9. 9)
      • 10. Nagy, A.M., Sweilam, N.H.: ‘An efficient method for solving fractional Hodgkin–Huxley model’, Phys. Lett. A, 2014, 378, pp. 1980–1984.
    10. 10)
      • 39. Dar, M.R., Kant, N.A., Khanday, F.A.: ‘Realization of Integrable incommensurate-fractional-order-Rössler-system design using operational transconductance amplifiers (OTAs) and its experimental verification’, Int. J. Bifurcation Chaos, 2017, 27, (5), pp. 1750077-1–1750077-15.
    11. 11)
      • 37. Tsirimokou, G., Psychalinos, C.: ‘Ultra-low voltage fractional-order differentiator and integrator topologies: an application for handling noisy ECGs’, Analog Integr. Circuits Signal Process., 2014, 81, (2), pp. 393–405.
    12. 12)
      • 3. Lundstrom, B.N., Higgs, M.H., Spain, W.J., et al: ‘Fractional differentiation by neocortical pyramidal neurons’, Nat. Neurosci., 2008, 11, (11), pp. 1335–1342.
    13. 13)
      • 25. Dahasert, N., Öztürk, I., Kiliç, R.: ‘Experimental realizations of the HR neuron model with programmable hardware and synchronization applications’, Nonlinear Dyn., 2012, 70, (4), pp. 2343–2358.
    14. 14)
      • 19. Kant, N.A., Dar, M.R., Khanday, F.A.: ‘An ultra-low-voltage electronic implementation of inertial neuron model with non-monotonous Liao's activation function’, Netw., Comput. Neural Syst., 2015, 26, (3–4), pp. 116–135.
    15. 15)
      • 17. Demirkol, A.S., Ozoguz, S.: ‘A low power VLSI implementation of the izhikevich neuron model’. IEEE 9th Int. New Circuits and Systems Conf., Bordeaux, France, 2011, pp. 169–172.
    16. 16)
      • 33. Dalibor, H.: ‘Synchronization of two Hindmarsh–Rose neurons with unidirectional coupling’, Neural Netw., 2013, 40, pp. 73–79.
    17. 17)
      • 42. Kant, N.A., Dar, M.R., Khanday, F.A., et al: ‘Ultra-low-voltage integrable electronic realization of integer- and fractional-order Liao's chaotic delayed neuron model’, Circuits Syst. Signal Process., 2017, 36, (12), pp. 4844–4868.
    18. 18)
      • 2. Ortigueira, M.: ‘An Introduction to the fractional continuous- time linear systems: the 21st century systems’, IEEE Circuits Syst. Mag., 2008, 8, (3), pp. 19–26.
    19. 19)
      • 22. Hayati, M., Nouri, M., Abbott, D., et al: ‘Digital multiplierless realization of two-coupled biological Hindmarsh–Rose neuron’, IEEE Trans. Circuits Syst. II, Express Briefs, 2016, 63, (5), pp. 463–467.
    20. 20)
      • 41. Dar, M.R., Kant, N.A., Khanday, F.A.: ‘Realization of fractional-order double-scroll chaotic system using operational transconductance amplifier (OTA)’, J. Circ. Syst. Comp., 2018, 27, (1), p. 1850006(15 pages). Available at https://doi.org/10.1142/S0218126618500068.
    21. 21)
      • 23. Hayati, M., Nouri, M., Haghiri, S., et al: ‘A digital realization of astrocyte and neural glial interactions’, IEEE Trans. Biomed. Circuits Syst., 2016, 10, (1), pp. 518–529.
    22. 22)
      • 32. Erdener, Ö, Ozoguz, S.: ‘A new neuron and synapse model suitable for low power VLSI implementation’, Analog Integr. Circuits Signal Process., 2016, 89, (3), pp. 749–770.
    23. 23)
      • 21. Nouri, M., Karimi, G.R., Ahmadi, A., et al: ‘Digital Multiplierless implementation of the biological FitzHugh-Nagumo model’, Neurocomputing, 2015, 165, pp. 468–476.
    24. 24)
      • 14. Ahmadi, P., Maundy, B., Elwakil, A.S., et al: ‘High-quality factor asymmetric-slope band-pass filters: a fractional-order capacitor approach’, IET Circuits Devices Syst., 2012, 6, (3), pp. 187–197.
    25. 25)
      • 13. Freeborn, T.J.: ‘A survey of fractional-order circuit models for biology and biomedicine’, IEEE J. Emerg. Sel. Top. Circuits Syst., 2013, 3, (3), pp. 416–424.
    26. 26)
      • 38. Tsirimokou, G., Laoudias, C., Psychalinos, C.: ‘0.5-V fractional-order companding filters’, Int. J. Circuit Theory Appl., 2015, 43, (9), pp. 105–1126.
    27. 27)
      • 1. Sabatier, J., Agrawal, O.P., Machado, J.A.T.: ‘Advances in fractional calculus: theoretical developments and applications in physics and engineering’ (Springer Publishing Company, Netherland, 2007), ISBN: 1402060416 9781402060410.
    28. 28)
      • 20. Hayati, M., Nouri, M., Haghiri, S., et al: ‘Digital Multiplierless realization of two coupled biological Morris-Lecar neuron model’, IEEE Trans. Circuits Syst. I, 2015, 62, (7), pp. 1805–1814.
    29. 29)
      • 27. Wang, H., Wang, Q., Qishao, L., et al: ‘Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction’, Cogn. Neurodynamics, 2013, 7, (2), pp. 121–131.
    30. 30)
      • 8. Yong, X., Mei, K.Y., Yong, L., et al: ‘Firing properties and synchronization rate in fractional-order Hindmarsh-Rose model neuron’, Sci. China Technol. Sci., 2014, 57, (5), pp. 914–922.
    31. 31)
      • 29. Yu, H., Peng, J.: ‘Chaotic synchronization and control in nonlinear coupled Hindmarsh–Rose neural systems’, Chaos Solitons Fractals, 2006, 29, (2), pp. 342–348.
    32. 32)
      • 31. Rose, R.M., Hindmarsh, J.L.: ‘The assembly of ionic currents in a thalamic neuron. I. The three-dimensional’, Proc. R. Soc. Lond. B, Biol. Sci., 1988, 22:237, (1288), pp. 267–288.
    33. 33)
      • 36. Lakshmanan, S., Lim, C.P., Nahavandi, S., et al: ‘Dynamical analysis of the Hindmarsh–Rose neuron with time delay’, IEEE Trans. Neural Netw. Learn. Syst., 2016, 28, (8), pp. 1953–1958.
    34. 34)
      • 15. Mondal, D., Biswas, K.: ‘Performance study of fractional order integrator using single-component fractional order element’, IET Circuits Devices Syst., 2011, 5, (4), pp. 334–342.
    35. 35)
      • 26. Djeundam, S.D., Yamapi, R., Filatrella, G., et al: ‘Stability of the synchronized network of Hindmarsh–Rose neuronal models with nearest and global couplings’, Commun. Nonlinear Sci. Numer. Simul., 2015, 22, (1–3), pp. 545–563.
    36. 36)
      • 5. Anastasio, T.J.: ‘The fractional-order dynamics of brainstem vestibulo-oculomotor neurons’, Biol. Cybern., 1994, 72, (1), pp. 69–79.
    37. 37)
      • 9. Velmurugan, G., Rakkiyappan, R.: ‘Stability analysis of fractional-order Hindmarsh-Rose neuron model with time-delays’, J. Int. Acad. Phys. Sci., 2015, 19, (3), pp. 233–243.
    38. 38)
      • 16. Hu, X., Liu, C., Liu, L., et al: ‘An electronic implementation for Morris–Lecar neuron model’, Nonlinear Dyn., 2016, 84, (4), pp. 2317–2332.
    39. 39)
      • 7. Yong, L., Yong, X.: ‘Dynamical characteristics of the fractional order Fitz-Hugh-Nagumo model neuron and its synchronization’, Acta Phys. Sin., 2010, 59, (3), pp. 2417–2455.
    40. 40)
      • 34. Matignon, D.: ‘Stability results for fractional differential equations with applications to control processing’, Proc. IEEE-SMC, 1996, 2, pp. 963–968.
    41. 41)
      • 40. Dar, M.R., Kant, N.A., Khanday, F.A.: ‘Electronic implementation of fractional order Newton-Leipnik chaotic system with application to communication’, J. Comput. Nonlinear Dyn., 2017, 12, (5), pp. 054502–054506.
    42. 42)
      • 12. Elwakil, A.: ‘Fractional-order circuits and systems: an emerging interdisciplinary research area’, IEEE Circuits Syst. Mag., 2010, 10, (4), pp. 40–50.
    43. 43)
      • 43. Freeborn, T.J., Maundy, B., Elwakil, A.S.: ‘Field programmable analogue array implementation of fractional step filters’, IET Circuits Devices Syst., 2010, 4, (6), pp. 514–524.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cds.2018.5033
Loading

Related content

content/journals/10.1049/iet-cds.2018.5033
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading