In this study, we investigated the impact of the asymmetry of a coupling scheme on oscillator dynamics in a star network. We obtained stability conditions for the collective behavior of the systems, ranging from an equilibrium point over complete synchronization (CS) and quenched hub incoherence to remote synchronization states using both numerical and analytical methods. The coupling asymmetry factor α significantly influences and determines the stable parameter region of each state. For α ≠ 1, the equilibrium point can emerge when the Hopf bifurcation parameter a is positive, which is impossible for diffusive coupling. However, CS can occur even if a is negative under α < 1. Unlike diffusive coupling, we observe more behavior when α ≠ 1, including additional in-phase remote synchronization. These results are supported by theoretical analysis and validated through numerical simulations and independent of network size. The findings may offer practical methods for controlling, restoring, or obstructing specific collective behavior.

1.
S. H.
Strogatz
,
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
(
CRC Press
,
2018
).
2.
A.
Pikovsky
,
M.
Rosenblum
, and
J.
Kurths
,
Synchronization: A Universal Concept in Nonlinear Science
(
Cambridge University Press
,
2002
).
3.
A.
Barrat
,
M.
Barthelemy
, and
A.
Vespignani
,
Dynamical Processes on Complex Networks
(
Cambridge University Press
,
2008
).
4.
A.
Koseska
,
E.
Volkov
, and
J.
Kurths
,
Phys. Rep.
531
,
173
(
2013
).
5.
W.
Zou
,
D.
Senthilkumar
,
M.
Zhan
, and
J.
Kurths
,
Phys. Rep.
931
,
1
(
2021
).
6.
W.
Zou
,
S.
He
, and
C.
Yao
,
Appl. Math. Lett.
131
,
108052
(
2022
).
7.
S.
Boccaletti
,
A. N.
Pisarchik
,
C. I.
Del Genio
, and
A.
Amann
,
Synchronization: From Coupled Systems to Complex Networks
(
Cambridge University Press
,
2018
).
8.
L.
Kocarev
,
Consensus and Synchronization in Complex Networks
(
Springer
,
2013
).
9.
J.
Sawicki
,
Delay Controlled Partial Synchronization in Complex Networks
(
Springer Nature
,
2019
).
10.
D.
Ghosh
,
M.
Frasca
,
A.
Rizzo
,
S.
Majhi
,
S.
Rakshit
,
K.
Alfaro-Bittner
, and
S.
Boccaletti
,
Phys. Rep.
949
,
1
(
2022
).
11.
S.
Liu
,
W.
Zou
,
M.
He
,
J.
Kurths
, and
M.
Zhan
,
SIAM J. Appl. Dyn. Syst.
16
,
1923
(
2017
).
12.
X.
Chen
,
X.
Liu
,
R.
Chen
,
F.
Li
, and
S.
Liu
,
Arch. Appl. Mech.
93
,
1095–1106
(
2023
).
13.
S.
Liu
,
X.
Chen
,
C.
Yao
, and
Z.
Zhang
,
Commun. Nonlinear Sci. Numer. Simul.
111
,
106456
(
2022
).
14.
A.
Bergner
,
M.
Frasca
,
G.
Sciuto
,
A.
Buscarino
,
E. J.
Ngamga
,
L.
Fortuna
, and
J.
Kurths
,
Phys. Rev. E
85
,
026208
(
2012
).
15.
M.
Frasca
,
A.
Bergner
,
J.
Kurths
, and
L.
Fortuna
,
Int. J. Bifurcation Chaos
22
,
1250173
(
2012
).
16.
A.
Arenas
,
A.
Díaz-Guilera
,
J.
Kurths
,
Y.
Moreno
, and
C.
Zhou
,
Phys. Rep.
469
,
93
(
2008
).
17.
R.
Arumugam
,
P. S.
Dutta
, and
T.
Banerjee
,
Phys. Rev. E
94
,
022206
(
2016
).
18.
T.
Banerjee
and
D.
Biswas
,
Nonlinear Dyn.
73
,
2025
(
2013
).
19.
Y.
Qin
,
Y.
Kawano
, and
M.
Cao
, in 2018 IEEE Conference on Decision and Control (CDC) (IEEE, 2018), pp. 5209–5214.
20.
J.
Lacerda
,
C.
Freitas
, and
E.
Macau
,
Appl. Math. Modell.
69
,
453
(
2019
).
21.
T.
Menara
,
Y.
Qin
,
D. S.
Bassett
, and
F.
Pasqualetti
,
IEEE Control Syst. Lett.
6
,
500
(
2021
).
22.
M.
Kumar
and
M.
Rosenblum
,
Phys. Rev. E
104
,
054202
(
2021
).
23.
Z.
Yang
,
D.
Chen
,
Q.
Xiao
, and
Z.
Liu
,
Chaos
32
,
103125
(
2022
).
24.
Y.
Qin
,
M.
Cao
,
B. D.
Anderson
,
D. S.
Bassett
, and
F.
Pasqualetti
,
IEEE Control Syst. Lett.
5
,
767
(
2020
).
25.
L.
Kang
,
Z.
Wang
,
S.
Huo
,
C.
Tian
, and
Z.
Liu
,
Nonlinear Dyn.
99
,
1577
(
2020
).
26.
V.
Nicosia
,
M.
Valencia
,
M.
Chavez
,
A.
Díaz-Guilera
, and
V.
Latora
,
Phys. Rev. Lett.
110
,
174102
(
2013
).
27.
X.
Chen
,
F.
Li
,
X.
Liu
, and
S.
Liu
,
Commun. Nonlinear Sci. Numer. Simul.
114
,
106674
(
2022
).
28.
W.
Zou
,
D.
Senthilkumar
,
R.
Nagao
,
I. Z.
Kiss
,
Y.
Tang
,
A.
Koseska
,
J.
Duan
, and
J.
Kurths
,
Nat. Commun.
6
,
7709
(
2015
).
29.
C.
Yao
and
Z.
He
,
Chaos
30
,
083120
(
2020
).
30.
L. M.
Pecora
and
T. L.
Carroll
,
Phys. Rev. Lett.
80
,
2109
(
1998
).
31.
T.
Banerjee
,
D.
Biswas
,
D.
Ghosh
,
B.
Bandyopadhyay
, and
J.
Kurths
,
Phys. Rev. E
97
,
042218
(
2018
).
32.
M. R.
Roussel
, in Nonlinear Dynamics: A Hands-On Introductory Survey (Morgan & Claypool Publishers, 2019).
33.
A. E.
Pereda
,
Nat. Rev. Neurosci.
15
,
250
(
2014
).
34.
T. C.
Südhof
and
R. C.
Malenka
,
Neuron
60
,
469
(
2008
).
35.
N.
Kopell
and
B.
Ermentrout
,
Proc. Natl. Acad. Sci. U.S.A.
101
,
15482
(
2004
).
36.
R.
Nagao
,
W.
Zou
,
J.
Kurths
, and
I. Z.
Kiss
,
Chaos
26
,
094808
(
2016
).
37.
D.
Ghosh
,
T.
Banerjee
, and
J.
Kurths
,
Phys. Rev. E
92
,
052908
(
2015
).
38.
K.
Kumar
,
D.
Biswas
,
T.
Banerjee
,
W.
Zou
,
J.
Kurths
, and
D.
Senthilkumar
,
Phys. Rev. E
100
,
052212
(
2019
).
You do not currently have access to this content.