We investigate the aging transition in networks of excitable and self-oscillatory units as the fraction of inherently excitable units increases. Two network topologies are considered: a scale-free network with weighted pairwise interactions and a two-dimensional simplicial complex with weighted scale-free pairwise and triadic interactions. Without triadic interactions, the aging transition from collective oscillations to oscillation death (inhomogeneous stationary states) can occur either suddenly or through an intermediate state of partial oscillation. However, when triadic interactions are present, the network becomes less resilient, and the transition occurs without partial oscillation at any coupling strength. Furthermore, we observe the presence of inhomogeneous steady states within the complete oscillation death regime, regardless of the network interaction models.
REFERENCES
1.
B.
Ermentrout
, Y.
Park
, and D.
Wilson
, “Recent advances in coupled oscillator theory
,” Phil. Trans. R. Soc. A
377
, 20190092
(2019
). 2.
J.
Miake
, E.
Marbán
, and H. B.
Nuss
, “Biological pacemaker created by gene transfer
,” Nature
419
, 132
–133
(2002
). 3.
F. A.
Dorfler
, Dynamics and Control in Power Grids and Complex Oscillator Networks
(University of California
, Santa Barbara
, 2013
).4.
A.
Pikovsky
, M.
Rosenblum
, and J.
Kurths
, “Synchronization: A universal concept in nonlinear sciences,” in Cambridge Nonlinear Science Series (Cambridge University Press, 2001).5.
H.
Daido
and K.
Nakanishi
, “Aging transition and universal scaling in oscillator networks
,” Phys. Rev. Lett.
93
, 104101
(2004
). 6.
G.
Tanaka
, K.
Morino
, and K.
Aihara
, “Dynamical robustness in complex networks: The crucial role of low-degree nodes
,” Sci. Rep.
2
, 232
(2012
). 7.
H.
Daido
and K.
Nakanishi
, “Aging and clustering in globally coupled oscillators
,” Phys. Rev. E
75
, 056206
(2007
). 8.
B.
Thakur
, D.
Sharma
, and A.
Sen
, “Time-delay effects on the aging transition in a population of coupled oscillators
,” Phys. Rev. E
90
, 042904
(2014
). 9.
S.
Kundu
, S.
Majhi
, S. K.
Sasmal
, D.
Ghosh
, and B.
Rakshit
, “Survivability of a metapopulation under local extinctions
,” Phys. Rev. E
96
, 062212
(2017
). 10.
S.
Majhi
, B.
Rakshit
, A.
Sharma
, J.
Kurths
, and D.
Ghosh
, “Dynamical robustness of network of oscillators
,” Phys. Rep.
1082
, 1
–46
(2024
). 11.
B.
Rakshit
, S.
Aryalakshmi
, A. J.
Kartha
, C.
Hens
et al., “Predicting aging transition using echo state network
,” Chaos
33
, 081102
(2023
). 12.
K.
Morino
, G.
Tanaka
, and K.
Aihara
, “Robustness of multilayer oscillator networks
,” Phys. Rev. E
83
, 056208
(2011
). 13.
A.
Sharma
and B.
Rakshit
, “Dynamical robustness in presence of attractive-repulsive interactions
,” Chaos, Solitons Fractals
156
, 111823
(2022
). 14.
Y.
Liu
, W.
Zou
, M.
Zhan
, J.
Duan
, and J.
Kurths
, “Enhancing dynamical robustness in aging networks of coupled nonlinear oscillators
,” Europhys. Lett.
114
, 40004
(2016
). 15.
S.
Kundu
, S.
Majhi
, and D.
Ghosh
, “Resumption of dynamism in damaged networks of coupled oscillators
,” Phys. Rev. E
97
, 052313
(2018
). 16.
B.
Rakshit
, N.
Rajendrakumar
, and B.
Balaram
, “Abnormal route to aging transition in a network of coupled oscillators
,” Chaos
30
, 101101
(2020
). 17.
A.
Sharma
and B.
Rakshit
, “Enhancement of dynamical robustness in a mean-field coupled network through self-feedback delay
,” Chaos
31
, 013114
(2021
). 18.
T.
Yuan
, K.
Aihara
, and G.
Tanaka
, “Robustness and fragility in coupled oscillator networks under targeted attacks
,” Phys. Rev. E
95
, 012315
(2017
). 19.
S.
Kundu
, S.
Majhi
, and D.
Ghosh
, “Chemical synaptic multiplexing enhances rhythmicity in neuronal networks
,” Nonlinear Dyn.
98
, 1659
–1668
(2019
). 20.
U.
Barać
, M.
Perc
, and M.
Gosak
, “Determinants of collective failure in excitable networks
,” Chaos
33
, 043120
(2023
). 21.
U.
Barać
, M.
Perc
, and M.
Gosak
, “Aging transitions of multimodal oscillators in multilayer networks
,” Phys. Rev. Res.
6
, 033269
(2024
). 22.
D.
Pazó
and E.
Montbrió
, “Universal behavior in populations composed of excitable and self-oscillatory elements
,” Phys. Rev. E
73
, 055202
(2006
). 23.
H.
Daido
, A.
Kasama
, and K.
Nishio
, “Onset of dynamic activity in globally coupled excitable and oscillatory units
,” Phys. Rev. E
88
, 052907
(2013
). 24.
H.
Daido
and K.
Nishio
, “Bifurcation and scaling at the aging transition boundary in globally coupled excitable and oscillatory units
,” Phys. Rev. E
93
, 052226
(2016
). 25.
I.
Ratas
and K.
Pyragas
, “Macroscopic self-oscillations and aging transition in a network of synaptically coupled quadratic integrate-and-fire neurons
,” Phys. Rev. E
94
, 032215
(2016
). 26.
J.
Guckenheimer
and P.
Holmes
, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
(Springer Science & Business Media
, 2013
), Vol. 42
.27.
Y. A.
Kuznetsov
, I. A.
Kuznetsov
, and Y.
Kuznetsov
, Elements of Applied Bifurcation Theory
(Springer
, 1998
), Vol. 112
.28.
F. C.
Hoppensteadt
and E. M.
Izhikevich
, Weakly Connected Neural Networks
(Springer Science & Business Media
, 2012
), Vol. 126
.29.
E.
Meron
, “Pattern formation in excitable media
,” Phys. Rep.
218
, 1
–66
(1992
). 30.
C.
Hens
, P.
Pal
, and S. K.
Dana
, “Bursting dynamics in a population of oscillatory and excitable Josephson junctions
,” Phys. Rev. E
92
, 022915
(2015
). 31.
S.
Ghosh
, A.
Mondal
, P.
Ji
, A.
Mishra
, S. K.
Dana
, C. G.
Antonopoulos
, and C.
Hens
, “Emergence of mixed mode oscillations in random networks of diverse excitable neurons: The role of neighbors and electrical coupling
,” Front. Comput. Neurosci.
14
, 49
(2020
). 32.
V.
Klinshov
and I.
Franović
, “Two scenarios for the onset and suppression of collective oscillations in heterogeneous populations of active rotators
,” Phys. Rev. E
100
, 062211
(2019
). 33.
D. L.
Barabási
, G.
Bianconi
, E.
Bullmore
, M.
Burgess
, S.
Chung
, T.
Eliassi-Rad
, D.
George
, I. A.
Kovács
, H.
Makse
, T. E.
Nichols
et al., “Neuroscience needs network science
,” J. Neurosci.
43
, 5989
–5995
(2023
). 34.
L.
Amaral
and J.
Ottino
, “Complex systems and networks: Challenges and opportunities for chemical and biological engineers
,” Chem. Eng. Sci.
59
, 1653
–1666
(2004
). 35.
V. M.
Eguiluz
, D. R.
Chialvo
, G. A.
Cecchi
, M.
Baliki
, and A. V.
Apkarian
, “Scale-free brain functional networks
,” Phys. Rev. Lett.
94
, 018102
(2005
). 36.
O.
Sporns
, D. R.
Chialvo
, M.
Kaiser
, and C. C.
Hilgetag
, “Organization, development and function of complex brain networks
,” Trends Cognit. Sci.
8
, 418
–425
(2004
). 37.
D. R.
Chialvo
, “Critical brain networks
,” Physica A
340
, 756
–765
(2004
). 38.
Q.
Wang
, M.
Perc
, Z.
Duan
, and G.
Chen
, “Synchronization transitions on scale-free neuronal networks due to finite information transmission delays
,” Phys. Rev. E
80
, 026206
(2009
). 39.
C.
Batista
, S. R.
Lopes
, R. L.
Viana
, and A. M.
Batista
, “Delayed feedback control of bursting synchronization in a scale-free neuronal network
,” Neural Netw.
23
, 114
–124
(2010
). 40.
X.
Hu
, Y.
Wu
, Q.
Ding
, Y.
Xie
, Z.
Ye
, and Y.
Jia
, “Synchronization of scale-free neuronal network with small-world property induced by spike-timing-dependent plasticity under time delay
,” Physica D
460
, 134091
(2024
). 41.
F.
Battiston
, G.
Cencetti
, I.
Iacopini
, V.
Latora
, M.
Lucas
, A.
Patania
, J.-G.
Young
, and G.
Petri
, “Networks beyond pairwise interactions: Structure and dynamics
,” Phys. Rep.
874
, 1
–92
(2020
). 42.
G.
Bianconi
, Higher-Order Networks
(Cambridge University Press
, 2021
).43.
S.
Yu
, H.
Yang
, H.
Nakahara
, G. S.
Santos
, D.
Nikolić
, and D.
Plenz
, “Higher-order interactions characterized in cortical activity
,” J. Neurosci.
31
, 17514
–17526
(2011
). 44.
S.
Stramaglia
, T.
Scagliarini
, B. C.
Daniels
, and D.
Marinazzo
, “Quantifying dynamical high-order interdependencies from the o-information: An application to neural spiking dynamics
,” Front. Physiol.
11
, 595736
(2021
). 45.
A.
Santoro
, F.
Battiston
, M.
Lucas
, G.
Petri
, and E.
Amico
, “Higher-order connectomics of human brain function reveals local topological signatures of task decoding, individual identification, and behavior,” bioRxiv 2023-12 (2023).46.
L.
Torres
, A. S.
Blevins
, D.
Bassett
, and T.
Eliassi-Rad
, “The why, how, and when of representations for complex systems
,” SIAM Rev.
63
, 435
–485
(2021
). 47.
P. S.
Skardal
and A.
Arenas
, “Abrupt desynchronization and extensive multistability in globally coupled oscillator simplexes
,” Phys. Rev. Lett.
122
, 248301
(2019
). 48.
I.
Iacopini
, G.
Petri
, A.
Barrat
, and V.
Latora
, “Simplicial models of social contagion
,” Nat. Commun.
10
, 2485
(2019
). 49.
Y.
Zhang
, M.
Lucas
, and F.
Battiston
, “Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes
,” Nat. Commun.
14
, 1605
(2023
). 50.
U.
Alvarez-Rodriguez
, F.
Battiston
, G. F.
de Arruda
, Y.
Moreno
, M.
Perc
, and V.
Latora
, “Evolutionary dynamics of higher-order interactions in social networks
,” Nat. Hum. Behav.
5
, 586
–595
(2021
). 51.
M. S.
Anwar
and D.
Ghosh
, “Neuronal synchronization in time-varying higher-order networks
,” Chaos
33
, 073111
(2023
). 52.
M. S.
Anwar
, N.
Frolov
, A. E.
Hramov
, and D.
Ghosh
, “Self-organized bistability on globally coupled higher-order networks
,” Phys. Rev. E
109
, 014225
(2024
). 53.
M.
Mehrabbeik
, S.
Jafari
, and M.
Perc
, “Synchronization in simplicial complexes of memristive Rulkov neurons
,” Front. Comput. Neurosci.
17
, 1248976
(2023
). 54.
F.
Parastesh
, M.
Mehrabbeik
, K.
Rajagopal
, S.
Jafari
, and M.
Perc
, “Synchronization in Hindmarsh–Rose neurons subject to higher-order interactions
,” Chaos
32
, 013125
(2022
). 55.
P.
Deivasundari
, H.
Natiq
, S.
He
, Y.
Peng
, and I.
Hussain
, “Synchronization in a higher-order neuronal network with blinking interactions
,” Eur. Phys. J. Spec. Top.
233
, 745
–755
(2024
).56.
C.
Morris
and H.
Lecar
, “Voltage oscillations in the barnacle giant muscle fiber
,” Biophys. J.
35
, 193
–213
(1981
). 57.
G.
Ermentrout
and N.
Kopell
, “Oscillator death in systems of coupled neural oscillators
,” SIAM J. Appl. Math.
50
, 125
–146
(1990
). 58.
Z.
He
, S.
Liu
, and M.
Zhan
, “Dynamical robustness analysis of weighted complex networks
,” Physica A
392
, 4181
–4191
(2013
). 59.
A. E.
Motter
, C.
Zhou
, and J.
Kurths
, “Network synchronization, diffusion, and the paradox of heterogeneity
,” Phys. Rev. E
71
, 016116
(2005
). 60.
U. K.
Verma
, A.
Sharma
, N. K.
Kamal
, J.
Kurths
, and M. D.
Shrimali
, “Explosive death induced by mean–field diffusion in identical oscillators
,” Sci. Rep.
7
, 7936
(2017
). 61.
H.
Bi
, X.
Hu
, X.
Zhang
, Y.
Zou
, Z.
Liu
, and S.
Guan
, “Explosive oscillation death in coupled Stuart-Landau oscillators
,” Europhys. Lett.
108
, 50003
(2014
). © 2025 Author(s). Published under an exclusive license by AIP Publishing.
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