We study numerically effects of time delay in networks of delay-coupled excitable FitzHugh–Nagumo systems with dissipation. Generation of periodic self-sustained oscillations and its threshold are analyzed depending on the dissipation of a single neuron, the delay time, and random initial conditions. The peculiarities of spatiotemporal dynamics of time-delayed bidirectional ring-structured FitzHugh–Nagumo neuronal systems are investigated in cases of local and nonlocal coupling topology between the nodes, and a first-order nonequilibrium phase transition to synchrony is established. It is shown that the emergence of an oscillatory activity in delay-coupled FitzHugh–Nagumo neurons is observed for smaller values of the coupling strength as the dissipation parameter decreases. This can provide the possibility of controlling the spatiotemporal behavior of the considered neuronal networks. The observed effects are quantified by plotting distributions of the maximal Lyapunov exponent and the global order parameter in terms of delay and coupling strength.
REFERENCES
1.
A. L.
Hodgkin
and A. F.
Huxley
, J. Physiol.
117
, 500
(1952
). 2.
R.
FitzHugh
, Biophys. J.
1
, 445
(1961
). 3.
J.
Nagumo
, S.
Arimoto
, and S.
Yoshizawa
, Proc. IRE
50
, 2061
(1962
). 4.
J.
Keener
and J.
Sneyd
, Mathematical Physiology
(Springer
, New York
, 1998
).5.
“Computational cell biology,” edited by C. P. Fall, E. S. Marland, J. M. Wagner, and J. J. Tyson (Springer New York, 2002).
6.
G. B.
Ermentrout
and D. H.
Terman
, Mathematical Foundations of Neuroscience
(Springer
, New York
, 2010
).7.
R.
Appali
, U.
van Rienen
, and T.
Heimburg
, in Advances in Planar Lipid Bilayers and Liposomes, Advances in Planar Lipid Bilayers and Liposomes Vol. 16 (Elsevier, 2012), pp. 275–299.8.
B.
Lindner
, Phys. Rev. Lett.
129
, 198101
(2022
). 9.
J. G.
Freire
and J. A. C.
Gallas
, Phys. Lett. A
375
, 1097
(2011
). 10.
Y.
Yao
and J.
Ma
, Eur. Phys. J. Plus
137
, 1214
(2022
). 11.
M. M.
Asl
, A.
Valizadeh
, and P. A.
Tass
, Front. Physiol.
9
, 1849
(2018
). 12.
A.
Knoblauch
and F. T.
Sommer
, Neurocomputing
52–54
, 301
(2003
). 13.
A.
Knoblauch
and F. T.
Sommer
, Neurocomputing
58–60
, 185
(2004
). 14.
J. E.
Desmedt
and G.
Cheron
, Electroencephalogr. Clin. Neurophysiol.
50
, 382
(1980
). 15.
Y.
Manor
, C.
Koch
, and I.
Segev
, Biophys. J.
60
, 1424
(1991
). 16.
S.
Boudkkazi
, E.
Carlier
, N.
Ankri
, O.
Caillard
, P.
Giraud
, L.
Fronzaroli-Molinieres
, and D.
Debanne
, Neuron
56
, 1048
(2007
). 17.
Q.
Wang
, M.
Perc
, Z.
Duan
, and G.
Chen
, Phys. Rev. E
80
, 026206
(2009
). 18.
G.
Stepan
, Philos. Trans. R. Soc. A
367
, 1059
(2009
). 19.
S.
Petkoski
and V. K.
Jirsa
, Philos. Trans. R. Soc. A
377
, 20180132
(2019
). 20.
A.
Pariz
, I.
Fischer
, A.
Valizadeh
, and C.
Mirasso
, PLoS Comput. Biol.
17
, e1008129
(2021
). 21.
A.
Balanov
, N.
Janson
, and E.
Schöll
, Physica D
199
, 1
(2004
). 22.
A. G.
Balanov
, V.
Beato
, N. B.
Janson
, H.
Engel
, and E.
Schöll
, Phys. Rev. E
74
, 1539
–3755
(2006
). 23.
E.
Schöll
, G.
Hiller
, P.
Hövel
, and M. A.
Dahlem
, Philos. Trans. R. Soc. A
367
, 1079
(2009
). 24.
O. V.
Popovych
, S.
Yanchuk
, and P. A.
Tass
, Phys. Rev. Lett.
107
, 228102
(2011
). 25.
M.
Kantner
, E.
Schöll
, and S.
Yanchuk
, Sci. Rep.
5
, 8522
(2015
). 26.
C.-U.
Choe
, T.
Dahms
, P.
Hövel
, and E.
Schöll
, Phys. Rev. E
81
, 025205
(2010
). 27.
Y. N.
Kyrychko
, K. B.
Blyuss
, and E.
Schöll
, Eur. Phys. J. B
84
, 307
(2011
). 28.
J.
Lehnert
, T.
Dahms
, P.
Hövel
, and E.
Schöll
, EPL
96
, 60013
(2011
). 29.
A.
Panchuk
, D. P.
Rosin
, P.
Hövel
, and E.
Schöll
, Int. J. Bifurcat. Chaos
23
, 1330039
(2013
). 30.
S. A.
Plotnikov
, J.
Lehnert
, A. L.
Fradkov
, and E.
Schöll
, Phys. Rev. E
94
, 012203
(2016
). 31.
C.
Wille
, J.
Lehnert
, and E.
Schöll
, Phys. Rev. E
90
, 032908
(2014
). 32.
Z. G.
Esfahani
and A.
Valizadeh
, PLoS One
9
, e112688
(2014
). 33.
Y. N.
Kyrychko
, K. B.
Blyuss
, and E.
Schöll
, Chaos
24
, 043117
(2014
). 34.
A.
Gjurchinovski
, A.
Zakharova
, and E.
Schöll
, Phys. Rev. E
89
, 032915
(2014
). 35.
Z. G.
Esfahani
, L. L.
Gollo
, and A.
Valizadeh
, Sci. Rep.
6
, 23471
(2016
). 36.
A.
Pariz
, Z. G.
Esfahani
, S. S.
Parsi
, A.
Valizadeh
, S.
Canals
, and C. R.
Mirasso
, NeuroImage
166
, 349
(2018
). 37.
A.
Ziaeemehr
, M.
Zarei
, A.
Valizadeh
, and C. R.
Mirasso
, Neural Netw.
132
, 155
(2020
). 38.
N.
Burić
and D.
Todorović
, Phys. Rev. E
67
, 066222
(2003
). 39.
M. A.
Dahlem
, G.
Hiller
, A.
Panchuk
, and E.
Schöll
, Int. J. Bifurc. Chaos
19
, 745
(2009
). 40.
O.
Vallès-Codina
, R.
Möbius
, S.
Rüdiger
, and L.
Schimansky-Geier
, Phys. Rev. E
83
, 036209
(2011
). 41.
J.
Tang
, J.
Ma
, M.
Yi
, H.
Xia
, and X.
Yang
, Phys. Rev. E
83
, 046207
(2011
). 42.
M.
Dhamala
, V. K.
Jirsa
, and M.
Ding
, Phys. Rev. Lett.
92
, 074104
(2004
). 43.
X.
Yang
, H.
Li
, and Z.
Sun
, PLoS One
12
, e0177918
(2017
). 44.
Y.
Wang
, X.
Zhang
, L.
Yang
, and H.
Huang
, Int. J. Control Autom. Syst.
18
, 696
(2020
). 45.
Y.
Kuramoto
and D.
Battogtokh
, Nonlinear Phenom. Complex Syst.
5
, 380
(2002
).46.
D. M.
Abrams
and S. H.
Strogatz
, Phys. Rev. Lett.
93
, 174102
(2004
). 47.
L.
Larger
, B.
Penkovsky
, and Y.
Maistrenko
, Phys. Rev. Lett.
111
, 054103
(2013
). 48.
V.
Semenov
, A.
Zakharova
, Y.
Maistrenko
, and E.
Schöll
, EPL
115
, 10005
(2016
). 49.
E.
Schöll
, Eur. Phys. J. Spec. Top.
225
, 891
(2016
). 50.
S.
Ghosh
, A.
Kumar
, A.
Zakharova
, and S.
Jalan
, EPL
115
, 60005
(2016
). 51.
A.
Gjurchinovski
, E.
Schöll
, and A.
Zakharova
, Phys. Rev. E
95
, 042218
(2017
). 52.
A.
Zakharova
, N.
Semenova
, V.
Anishchenko
, and E.
Schöll
, Chaos
27
, 114320
(2017
). 53.
J.
Sawicki
, I.
Omelchenko
, A.
Zakharova
, and E.
Schöll
, Eur. Phys. J. Spec. Top.
226
, 1883
(2017
). 54.
J.
Sawicki
, I.
Omelchenko
, A.
Zakharova
, and E.
Schöll
, Phys. Rev. E
98
, 062224
(2018
). 55.
J.
Sawicki
, S.
Ghosh
, S.
Jalan
, and A.
Zakharova
, Front. Appl. Math. Stat.
5
, 19
(2019
). 56.
D.
Nikitin
, I.
Omelchenko
, A.
Zakharova
, M.
Avetyan
, A. L.
Fradkov
, and E.
Schöll
, Philos. Trans. R. Soc. A
377
, 20180128
(2019
). 57.
J.
Sawicki
, I.
Omelchenko
, A.
Zakharova
, and E.
Schöll
, Eur. Phys. J. B
92
, 54
(2019
). 58.
A.
Zakharova
, Chimera Patterns in Networks
(Springer International Publishing
, 2020
).59.
A. S.
Tchakoutio Nguetcho
, S.
Binczak
, V. B.
Kazantsev
, S.
Jacquir
, and J.-M.
Bilbault
, Nonlinear Dyn.
82
, 1595
(2015
). 60.
E. M.
Izhikevich
and R.
FitzHugh
, Scholarpedia
1
, 1349
(2006
). 61.
M. A.
Dahlem
, F. M.
Schneider
, and E.
Schöll
, J. Theor. Biol.
251
, 202
(2008
). 62.
V. I.
Nekorkin
, D. S.
Shapin
, A. S.
Dmitrichev
, V. B.
Kazantsev
, S.
Binczak
, and J. M.
Bilbault
, Physica D
237
, 2463
(2008
). 63.
V. B.
Kazantsev
, Phys. Rev. E
64
, 056210
(2001
). 64.
V. I.
Nekorkin
, A. S.
Dmitrichev
, D. S.
Shchapin
, and V. B.
Kazantsev
, Mat. Model.
17
, 75
(2005
).65.
I. A.
Shepelev
, D. V.
Shamshin
, G. I.
Strelkova
, and T. E.
Vadivasova
, Chaos, Solitons Fractals
104
, 153
(2017
). 66.
H.
Rezaei
, A.
Aertsen
, A.
Kumar
, and A.
Valizadeh
, PLoS Comput. Biol.
16
, e1008033
(2020
). 67.
S.
Lenhert
, Biophys. J.
100
, 507a
(2011
). 68.
C. R.
Laing
and O.
Omel’chenko
, Chaos
30
, 043117
(2020
). 69.
H.
Schmidt
and D.
Avitabile
, Chaos
30
, 033133
(2020
). 70.
J.
Fialkowski
, S.
Yanchuk
, I. M.
Sokolov
, E.
Schöll
, G. A.
Gottwald
, and R.
Berner
, Phys. Rev. Lett.
130
, 067402
(2023
). 71.
L.
Tumash
, S.
Olmi
, and E.
Schöll
, EPL
123
, 20001
(2018
). © 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.