A biomorphic neuron model and principles of designing a neural network with memristor synapses for a biomorphic neuroprocessor

  • V. A. Filippov
  • A. N. Bobylev
  • A. N. BusyginEmail author
  • A. D. Pisarev
  • S. Yu. Udovichenko
Original Article


This paper presents an original biomorphic neuron model, which differs from common IT models by a more complex synapse structure and from biological models by replacement of differential equations that describe the change in potential over time with explicit recurrence expressions by approximation of experimental data in the cortical neuron, and therefore, by transition from the spiking information coding to the coding using the average frequency of action potentials per a simulation step. This approach ensures sufficiently simple and efficient calculation of an ultra-large neural network in the stand-alone hardware with limited computing resources. The model consists of three separate functional parts: dendrites, soma, and axon, which allows implementing any connections between functional parts of different neurons, thus making the neural network architecture more flexible. To perform functional testing of the neuron model, the test neural network performing simple association and constructed as a consequent stack of functional blocks with primary connections organized using experimental neurophysiological data was simulated. It is shown that encoding of the information transmitted by the impulses, similar to biological ones, allows using memristors for calculating recurrence expressions that describe the change in the quantity of neurotransmitter receptors of the dendrite membrane. The elaborated biomorphic neuron model, defined conceptual principles of a neural network construction based on it, as well as replacement of synapses in the neural network with memristors will allow building an ultra-large biomorphic neural network that simulates the functioning of a separate brain cortical column in the stand-alone hardware—a biomorphic neuroprocessor.


Biomorphic neuron model Biomorphic neural network Memristor Memristor-based synapses 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Udovichenko SY, Pisarev AD, Busygin AN, Maevsky OV (2018) Neuroprocessor based on combined memristor-diode crossbar. Nanoindustry 5:344–355. CrossRefGoogle Scholar
  2. 2.
    Pisarev A, Busygin A, Udovichenko S, Maevsky O (2018) 3D memory matrix based on a composite memristor-diode crossbar for a neuromorphic processor. Microelectron Eng 198:1–7. CrossRefGoogle Scholar
  3. 3.
    Udovichenko S, Pisarev A, Busygin A, Maevsky O (2017) 3D CMOS memristor nanotechnology for creating logical and memory matrices of neuroprocessor. Nanoindustry 5:26–34. CrossRefGoogle Scholar
  4. 4.
    Maevsky OV, Pisarev AD, Busygin AN, Udovichenko SY (2018) Complementary memristor-diode cell for a memory matrix in neuromorphic processor. Int J Nanotechnol 15(4/5):388–393. Google Scholar
  5. 5.
    Pisarev AD, Busygin AN, Udovichenko SYu, Bobylev AN, Maevsky OV (2018) A biomorphic neuroprocessor based on the composite memristor-diode crossbar. Book of abstracts of international workshop from RERAM and Memristors to new Computing Paradigms (MEM-Q):25Google Scholar
  6. 6.
    Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544. CrossRefGoogle Scholar
  7. 7.
    Merolla РА, Arthur JV, Alvarez-Icaza R et al (2014) A million spiking-neuron integrated circuit with a scalable communication network and interface. Science 345:668–672. CrossRefGoogle Scholar
  8. 8.
    Prezioso M, Merrikh-Bayat F, Hoskins BD, Adam GC, Likharev KK, Strukov DB (2015) Training and operation of an integrated neuromorphic network based on metal-oxide memristors. Nature 521:61–64. CrossRefGoogle Scholar
  9. 9.
    Kim K-H, Gaba S, Wheeler D, Cruz-Albrecht JM, Hussain T, Srinivasa N, Lu W (2012) A functional hybrid memristor crossbar-array/CMOS system for data storage and neuromorphic applications. Nano Lett 12:389–395. CrossRefGoogle Scholar
  10. 10.
    Bobylev AN, Busygin AN, Pisarev AD, Udovichenko SYu, Filippov VA (2017) Neuromorphic coprocessor prototype based on mixed metal oxide memristors. Int J Nanotechnol 14(7/8):698–704. CrossRefGoogle Scholar
  11. 11.
    Govoreanu B, Kar GS, Chen Y-Y et al. (2011) 10 × 10 nm2 Hf/HfOx crossbar resistive RAM with excellent performance, reliability and low-energy operation. In: Proceedings of 2011 IEEE international electron devices meeting (IEDM), pp 31.6.1–31.6.4.
  12. 12.
    Bobylev AN, Udovichenko SYu (2016) The electrical properties of memristor devices TiN/TixAl1−xOy/TiN produced by magnetron sputtering. Russ Microlectron 45(6):396–401. CrossRefGoogle Scholar
  13. 13.
    Jo SH, Chang T, Ebong I et al (2010) Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett 10(4):1297–1301. CrossRefGoogle Scholar
  14. 14.
    Wang Z, Wang X (2018) A novel memristor-based circuit implementation of full-function Pavlov associative memory accorded with biological feature. IEEE Trans Circuits Syst I Regul Pap 65(7):2210–2220. CrossRefGoogle Scholar
  15. 15.
    Yang L, Zeng Z, Huang Y, Wen S (2018) Memristor-based circuit implementations of recognition network and recall network with forgetting stages. IEEE Trans Cogn Dev Syst 10(4):1133–1142. CrossRefGoogle Scholar
  16. 16.
    Zhang X, Long K (2019) Improved learning experience memristor model and application as neural network synapse. IEEE Access 7:15262–15271. CrossRefGoogle Scholar
  17. 17.
    Wang Z, Rao M, Han J-W et al (2018) Capacitive neural network with neuro-transistors. Nat Commun 9:3208. CrossRefGoogle Scholar
  18. 18.
    Liu J, Huang Y, Luo Y, Harkin J, McDaid L (2019) Bio-inspired fault detection circuits based on synapse and spiking neuron models. Neurocomputing 331:473–482. CrossRefGoogle Scholar
  19. 19.
    Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 534(7191):80–83. CrossRefGoogle Scholar
  20. 20.
    Liu J, Harkin J, Maguire LP et al (2017) SPANNER: a self-repairing spiking neural network hardware architecture. IEEE Trans Neural Netw Learn Syst 29(4):1287–1300. CrossRefGoogle Scholar
  21. 21.
    Liu J, McDaid LJ, Harkin J et al (2018) Exploring self-repair in a coupled spiking astrocyte neural network. IEEE Trans Neural Netw Learn Syst 30(3):865–875. CrossRefGoogle Scholar
  22. 22.
    Rosenblatt F (1958) The perceptron: a probabilistic model for information storage and organization in the brain. Psychol Rev 65:386–408. CrossRefGoogle Scholar
  23. 23.
    Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61:85–117. CrossRefGoogle Scholar
  24. 24.
    Filippov VA (2008) Chapter 5. Neuron modeling. In: Sokolova EN, Filippov VA, Chernorizov AM (ed) Neuron. Signal processing. Plasticity. Modeling. Fundamental guide. Publishing house of Tyumen State University, Tyumen, Russia, pp 468–535.
  25. 25.
    Geminiani A, Casellato C, Locatelli F et al (2018) Complex dynamics in simplified neuronal models: reproducing golgi cell electroresponsiveness. Front Neuroinform 12:88. CrossRefGoogle Scholar
  26. 26.
    Blundell I, Plotnikov D, Eppler JM, Morrison A (2018) Automatically selecting a suitable integration scheme for systems of differential equations in neuron models. Front Neuroinform 12:50. CrossRefGoogle Scholar
  27. 27.
    Fox K (2017) Deconstructing the cortical column in the barrel cortex. Neuroscience 368:17–28. CrossRefGoogle Scholar
  28. 28.
    Malebra P, Rulkov NF, Bazhenov M (2019) Large time step discrete-time modeling of sharp wave activity in hippocampal area CA3. Commun Nonlinear Sci Numer Simulat 72:162–175. MathSciNetCrossRefGoogle Scholar
  29. 29.
    Brette R (2015) Philosophy of the spike: rate-based vs. spike-based theories of the brain. Front Syst Neurosci 9:151. CrossRefGoogle Scholar
  30. 30.
    Touboul J, Brette R (2008) Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. Biol Cybern 99:319–334. MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Rulkov NF, Neiman AB (2018) Control of sampling rate in map-based models of spiking neurons. Commun Nonlinear Sci Numer Simulat 61:127–137. MathSciNetCrossRefGoogle Scholar
  32. 32.
    Komarov M, Krishnan G, Chauvette S et al (2018) New class of reduced computationally efficient neuronal models for large-scale simulations of brain dynamics. J Comput Neurosci 44:1–24. MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Winters BD, Jin S-X, Ledford KR, Golding NL (2017) Amplitude normalization of dendritic EPSPs at the soma of binaural coincidence detector neurons of the medial superior olive. J Neurosci 37(12):3138–3149. CrossRefGoogle Scholar
  34. 34.
    Timofeeva Yu, Volynski KE (2015) Calmodulin as a major calcium buffer shaping vesicular release and short-term synaptic plasticity: facilitation through buffer dislocation. Front Cell Neurosci 9:239. CrossRefGoogle Scholar
  35. 35.
    Pickett MD, Strukov DB, Borghetti JL, Yang J, Snider GS, Stewart DR, Williams RS (2009) Switching dynamics in titanium dioxide memristive devices. J Appl Phys 106(7):074508. CrossRefGoogle Scholar
  36. 36.
    Bean BP (2007) The action potential in mammalian central neurons. Nat Rev Neurosci 8:451–465. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • V. A. Filippov
    • 1
  • A. N. Bobylev
    • 2
  • A. N. Busygin
    • 2
    Email author
  • A. D. Pisarev
    • 2
  • S. Yu. Udovichenko
    • 2
  1. 1.Organization of Cognitive Associative Systems (OCAS), LLCTyumenRussia
  2. 2.REC “Nanotechnology”University of TyumenTyumenRussia

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