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.

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
).
You do not currently have access to this content.