We investigate a spike activity of a network of excitable FitzHugh–Nagumo neurons, which is under constant two-frequency auditory signals. The neurons are supplemented with linear frequency filters and nonlinear input signal converters. We show that it is possible to configure the network to recognize a specific frequency ratio (musical interval) by selecting the parameters of the neurons, input filters, and coupling between neurons. A set of appropriately configured subnetworks with different topologies and coupling strengths can serve as a classifier for musical intervals. We have found that the selective properties of the classifier are due to the presence of a specific topology of coupling between the neurons of the network.
REFERENCES
1.
X.
Yao
, “A review of evolutionary artificial neural networks
,” Int. J. Intell. Syst.
8
, 539
–567
(1993
). 2.
M. G.
Abdolrasol
, S. S.
Hussain
, T. S.
Ustun
, M. R.
Sarker
, M. A.
Hannan
, R.
Mohamed
, J. A.
Ali
, S.
Mekhilef
, and A.
Milad
, “Artificial neural networks based optimization techniques: A review
,” Electronics
10
, 2689
(2021
). 3.
A.
Nguyen
, J.
Yosinski
, and J.
Clune
, “Deep neural networks are easily fooled: High confidence predictions for unrecognizable images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2015), pp. 427–436.4.
D. L.
Marino
, K.
Amarasinghe
, and M.
Manic
, “Building energy load forecasting using deep neural networks,” in IECON 2016-42nd Annual Conference of the IEEE Industrial Electronics Society (IEEE, 2016), pp. 7046–7051.5.
H. C.
Tuckwell
and R.
Rodriguez
, “Analytical and simulation results for stochastic FitzHugh-Nagumo neurons and neural networks
,” J. Comput. Neurosci.
5
, 91
–113
(1998
). 6.
J.
Cabral
, M. L.
Kringelbach
, and G.
Deco
, “Exploring the network dynamics underlying brain activity during rest
,” Prog. Neurobiol.
114
, 102
–131
(2014
). 7.
H.
Schmidt
, G.
Petkov
, M. P.
Richardson
, and J. R.
Terry
, “Dynamics on networks: The role of local dynamics and global networks on the emergence of hypersynchronous neural activity
,” PLoS Comput. Biol.
10
, e1003947
(2014
). 8.
C.
Bick
, M.
Goodfellow
, C. R.
Laing
, and E. A.
Martens
, “Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: A review
,” J. Math. Neurosci.
10
, 9
(2020
). 9.
A.
Prieto
, B.
Prieto
, E. M.
Ortigosa
, E.
Ros
, F.
Pelayo
, J.
Ortega
, and I.
Rojas
, “Neural networks: An overview of early research, current frameworks and new challenges
,” Neurocomputing
214
, 242
–268
(2016
). 10.
W.
Maass
, “Networks of spiking neurons: The third generation of neural network models
,” Neural Netw.
10
, 1659
–1671
(1997
). 11.
S.
Ghosh-Dastidar
and H.
Adeli
, “Spiking neural networks
,” Int. J. Neural Syst.
19
, 295
–308
(2009
). 12.
W.
Maass
, “Lower bounds for the computational power of networks of spiking neurons
,” Neural Comput.
8
, 1
–40
(1996
). 13.
W.
Maass
, “Fast sigmoidal networks via spiking neurons
,” Neural Comput.
9
, 279
–304
(1997
). 14.
R.
Gütig
, “To spike, or when to spike?
,” Curr. Opin. Neurobiol.
25
, 134
–139
(2014
). 15.
M.
Beyeler
, N. D.
Dutt
, and J. L.
Krichmar
, “Categorization and decision-making in a neurobiologically plausible spiking network using a STDP-like learning rule
,” Neural Netw.
48
, 109
–124
(2013
). 16.
S. R.
Kulkarni
and B.
Rajendran
, “Spiking neural networks for handwritten digit recognition—Supervised learning and network optimization
,” Neural Netw.
103
, 118
–127
(2018
). 17.
H. C.
Tuckwell
, “Synaptic transmission in a model for stochastic neural activity
,” J. Theor. Biol.
77
, 65
–81
(1979
). 18.
E. M.
Izhikevich
, “Simple model of spiking neurons
,” IEEE Trans. Neural Netw.
14
, 1569
–1572
(2003
). 19.
R.
Rose
and J.
Hindmarsh
, “The assembly of ionic currents in a thalamic neuron. I. The three-dimensional model
,” Proc. R. Soc. London B Biol. Sci.
237
, 267
–288
(1989
). 20.
A. L.
Hodgkin
and A. F.
Huxley
, “A quantitative description of membrane current and its application to conduction and excitation in nerve
,” J. Physiol.
117
, 500
(1952
). 21.
R.
FitzHugh
, “Impulses and physiological states in theoretical models of nerve membrane
,” Biophys. J.
1
, 445
–466
(1961
). 22.
J.
Nagumo
, S.
Arimoto
, and S.
Yoshizawa
, “An active pulse transmission line simulating nerve axon
,” Proc. IRE
50
, 2061
–2070
(1962
). 23.
F.
Ponulak
and A.
Kasiński
, “Supervised learning in spiking neural networks with resume: Sequence learning, classification, and spike shifting
,” Neural Comput.
22
, 467
–510
(2010
). 24.
A.
Tavanaei
, M.
Ghodrati
, S. R.
Kheradpisheh
, T.
Masquelier
, and A.
Maida
, “Deep learning in spiking neural networks
,” Neural Netw.
111
, 47
–63
(2019
). 25.
R. E.
Turkson
, H.
Qu
, C. B.
Mawuli
, and M. J.
Eghan
, “Classification of Alzheimer’s disease using deep convolutional spiking neural network
,” Neural Process. Lett.
53
, 2649
–2663
(2021
). 26.
E. O.
Neftci
, H.
Mostafa
, and F.
Zenke
, “Surrogate gradient learning in spiking neural networks: Bringing the power of gradient-based optimization to spiking neural networks
,” IEEE Signal Process. Mag.
36
, 51
–63
(2019
). 27.
C.
Lee
, S. S.
Sarwar
, P.
Panda
, G.
Srinivasan
, and K.
Roy
, “Enabling spike-based backpropagation for training deep neural network architectures
,” Front. Neurosci.
14
, 497482
(2020
). 28.
S.
Song
, K. D.
Miller
, and L. F.
Abbott
, “Competitive Hebbian learning through spike-timing-dependent synaptic plasticity
,” Nat. Neurosci.
3
, 919
–926
(2000
). 29.
J.
Wu
, Y.
Chua
, M.
Zhang
, H.
Li
, and K. C.
Tan
, “A spiking neural network framework for robust sound classification
,” Front. Neurosci.
12
, 379777
(2018
). 30.
A.
Tavanaei
and A. S.
Maida
, “Training a hidden Markov model with a Bayesian spiking neural network
,” J. Signal Process. Syst.
90
, 211
–220
(2018
). 31.
J. J.
Wade
, L. J.
McDaid
, J. A.
Santos
, and H. M.
Sayers
, “SWAT: A spiking neural network training algorithm for classification problems
,” IEEE Trans. Neural Netw.
21
, 1817
–1830
(2010
). 32.
J.
Wu
, C.
Xu
, X.
Han
, D.
Zhou
, M.
Zhang
, H.
Li
, and K. C.
Tan
, “Progressive tandem learning for pattern recognition with deep spiking neural networks
,” IEEE Trans. Pattern Anal. Mach. Intell.
44
, 7824
–7840
(2021
). 33.
Z.
Pan
, M.
Zhang
, J.
Wu
, J.
Wang
, and H.
Li
, “Multi-tone phase coding of interaural time difference for sound source localization with spiking neural networks
,” IEEE/ACM Trans. Audio, Speech, Lang. Process.
29
, 2656
–2670
(2021
). 34.
G. A.
Mashour
, P.
Roelfsema
, J.-P.
Changeux
, and S.
Dehaene
, “Conscious processing and the global neuronal workspace hypothesis
,” Neuron
105
, 776
–798
(2020
). 35.
G.
Tononi
, M.
Boly
, M.
Massimini
, and C.
Koch
, “Integrated information theory: From consciousness to its physical substrate
,” Nat. Rev. Neurosci.
17
, 450
–461
(2016
). 36.
C. M.
Signorelli
and D.
Meling
, “Towards new concepts for a biological neuroscience of consciousness
,” Cogn. Neurodyn.
15
, 783
–804
(2021
). 37.
B. A.
Siebert
, C. L.
Hall
, J. P.
Gleeson
, and M.
Asllani
, “Role of modularity in self-organization dynamics in biological networks
,” Phys. Rev. E
102
, 052306
(2020
). 38.
T.
Menara
, G.
Baggio
, D.
Bassett
, and F.
Pasqualetti
, “Functional control of oscillator networks
,” Nat. Commun.
13
, 4721
(2022
). 39.
P.
Feketa
, A.
Schaum
, and T.
Meurer
, “Synchronization and multicluster capabilities of oscillatory networks with adaptive coupling
,” IEEE Trans. Autom. Control
66
, 3084
–3096
(2020
). 40.
I.
Shepelev
, A.
Bukh
, S.
Muni
, and V.
Anishchenko
, “Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators
,” Chaos, Solitons Fractals
135
, 109725
(2020
). 41.
I. A.
Shepelev
, S. S.
Muni
, E.
Schöll
, and G. I.
Strelkova
, “Repulsive inter-layer coupling induces anti-phase synchronization
,” Chaos
31
, 063116
(2021
). 42.
E.
Rybalova
, G.
Strelkova
, and V.
Anishchenko
, “Impact of sparse inter-layer coupling on the dynamics of a heterogeneous multilayer network of chaotic maps
,” Chaos, Solitons Fractals
142
, 110477
(2021
). 43.
P. S.
Skardal
and A.
Arenas
, “Memory selection and information switching in oscillator networks with higher-order interactions
,” J. Phys.: Complex.
2
, 015003
(2020
). 44.
L.
Guo
, D.
Liu
, Y.
Wu
, and G.
Xu
, “Comparison of spiking neural networks with different topologies based on anti-disturbance ability under external noise
,” Neurocomputing
529
, 113
–127
(2023
). 45.
Y.
Mao
and H.
Dankowicz
, “Topology-dependent excitation response of networks of linear and nonlinear oscillators
,” J. Comput. Nonlinear Dyn.
16
, 041001
(2021
). 46.
B.
Al Beattie
, P.
Feketa
, K.
Ochs
, and H.
Kohlstedt
, “Criticality in Fitzhugh-Nagumo oscillator ensembles: Design, robustness, and spatial invariance
,” Commun. Phys.
7
, 46
(2024
). 47.
E.
Prout
, “Chapter I. Introduction,” in Harmony: Its Theory and Practice, Cambridge Library Collection-Music (Cambridge University Press, 1903), pp. 1–12.48.
M.
Yanagita
, “BMP antagonists: Their roles in development and involvement in pathophysiology
,” Cytokine Growth Factor Rev.
16
, 309
–317
(2005
). © 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.