Abstract
Fixed-time synchronization of fractional-order multilayer complex networks is studied in this paper. At first, a novel fixed-time stability theorem for the fractional-order nonlinear system is presented. The stability theorem is a generalization of the integer order stability theorem and plays an important role on the synchronization schemes. Based on the proposed stability theorem, the fixed-time synchronization of fractional-order multilayer complex networks is investigated, and a fixed-time synchronization criterion is presented. Simulation results are given to demonstrate the effectiveness of our results.
Issue Section:
Research Papers
References
1.
Gong
,
S. Q.
,
Guo
,
Z. Y.
,
Wen
,
S. P.
, and
Huang
,
T. W.
, 2021
, “
Finite-Time and Fixed-Time Synchronization of Coupled Memristive Neural Networks With Time Delay
,” IEEE Trans. Cybern.
,
51
(6
), pp. 2944
–2955
.10.1109/TCYB.2019.29532362.
Radicchi
,
F.
, and
Arenas
,
A.
, 2013
, “
Abrupt Transition in the Structural Formation of Interconnected Networks
,” Nat. Phys.
,
9
(11
), pp. 717
–720
.10.1038/nphys27613.
Dabiri
,
A.
,
Karimi Chahrogh
,
L.
, and
Tenreiro Machado
,
J. A.
, 2021
, “
Consensus of Incommensurate-Order Fractional Multiagent Systems With a Fixed-Length Memory
,” 2021 American Control Conference (ACC)
, New Orleans, LA
, May 25–28
, pp. 3320
–3325
.10.23919/ACC50511.2021.94828724.
Yin
,
X.
,
Yue
,
D.
, and
Hu
,
S.
, 2013
, “
Consensus of Fractional-Order Heterogeneous Multi-Agent Systems
,” IET Control Theory Appl.
,
7
(2
), pp. 314
–322
.10.1049/iet-cta.2012.05115.
Syed Ali
,
M.
,
Narayanan
,
G.
,
Saroha
,
S.
,
Priya
,
B.
, and
Thakur
,
G. K.
, 2021
, “
Finite-Time Stability Analysis of Fractional-Order Memristive Fuzzy Cellular Neural Networks With Time Delay and Leakage Term
,” Math. Comput. Simul.
,
185
, pp. 468
–485
.10.1016/j.matcom.2020.12.0356.
Zhang
,
X.
,
Tang
,
L. K.
, and
Lü
,
J. H.
, 2020
, “
Synchronization Analysis on Two-Layer Networks of Fractional-Order Systems: Intraiayer and Interiayer Synchronization
,” IEEE Trans. Circuits Syst.
,
67
(7
), pp. 2397
–2408
.10.1109/TCSI.2020.29716087.
Yang
,
S.
,
Hu
,
C.
,
Yu
,
J.
, and
Jiang
,
H. J.
, 2021
, “
Projective Synchronization in Finite-Time for Fully Quaternion-Valued Memristive Networks With Fractional-Order, Chaos
,” Solitons Fractals
,
147
, p. 110911
.10.1016/j.chaos.2021.1109118.
Wu
,
X. F.
,
Bao
,
H. B.
, and
Cao
,
J. D.
, 2021
, “
Finite-Time Inter-Layer Projective Synchronization of Caputo Fractional-Order Two-Layer Networks by Sliding Mode Control
,” J. Franklin Inst.
,
358
(1
), pp. 1002
–1020
.10.1016/j.jfranklin.2020.10.0439.
Wu
,
X. F.
, and
Bao
,
H. B.
, 2020
, “
Finite Time Complete Synchronization for Fractional-Order Multiplex Networks
,” Appl. Math. Comput.
,
377
, p. 125188
.10.
Yang
,
Y.
,
Hu
,
C.
,
Yu
,
J.
,
Jiang
,
H.
, and
Wen
,
S.
, 2021
, “
Synchronization of Fractional-Order Spatiotemporal Complex Networks With Boundary Communication
,” Neurocomputing
,
450
, pp. 197
–207
.10.1016/j.neucom.2021.04.00811.
Stamova
,
I.
, and
Stamov
,
G.
, 2017
, “
Mittag-Leffler Synchronization of Fractional Neural Networks With Time-Varying Delays and Reaction-Diffusion Terms Using Impulsive and Linear Controllers
,” Neural Networks
,
96
, pp. 22
–32
.10.1016/j.neunet.2017.08.00912.
Soriano-SáNchez
,
A. G.
,
Posadas-Castillo
,
C.
,
Platas-Garza
,
M. A.
, and
Arellano-Delgado
,
A.
, 2018
, “
Synchronization and FPGA Realization of Complex Networks With Fractional - Order Liu Chaotic Oscillators
,” Appl. Math. Comput.
,
332
, pp. 250
–262
.https://www.sciencedirect.com/science/article/abs/pii/S002626921831003613.
Li
,
H. L.
,
Cao
,
J. D.
,
Jiang
,
H. J.
, and
Alsaedi
,
A.
, 2018
, “
Graph Theory-Based Finite-Time Synchronization of Fractional-Order Complex Dynamical Networks
,” J. Franklin Inst.
,
355
(13
), pp. 5771
–5789
.10.1016/j.jfranklin.2018.05.03914.
Polyakov
,
A.
, 2012
, “
Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems
,” IEEE Trans. Autom. Control
,
57
(8
), pp. 2106
–2110
.10.1109/TAC.2011.217986915.
Arslan
,
E.
,
Narayanan
,
G.
,
Syed Ali
,
M.
,
Arik
,
S.
, and
Saroha
,
S.
, 2020
, “
Controller Design for Finite-Time and Fixed-Time Stabilization of Fractional-Order Memristive Complex-Valued BAM Neural Networks With Uncertain Parameters and Time-Varying Delays
,” Neural Networks
,
130
, pp. 60
–74
.10.1016/j.neunet.2020.06.02116.
Shirkavand
,
M.
,
Pourgholi
,
M.
, and
Yazdizadeh
,
A.
, 2019
, “
Robust Fixed-Time Synchronisation of Non-Identical Nodes in Complex Networks Under Input Non-Linearities
,” IET Control Theory Appl.
,
13
(13
), pp. 2095
–2103
.10.1049/iet-cta.2018.628717.
Zhou
,
L. L.
,
Tan
,
F.
,
Li
,
X. H.
, and
Zhou
,
L.
, 2021
, “
A Fixed-Time Synchronization-Based Secure Communication Scheme for Two-Layer Hybrid Coupled Networks
,” Neurocomputing
,
433
, pp. 131
–141
.10.1016/j.neucom.2020.12.03318.
Alimi
,
A. M.
,
Aouiti
,
C.
, and
Assali
,
E.
, 2019
, “
Finite-Time and Fixed-Time Synchronization of a Class of Inertial Neural Networks With Multi-Proportional Delays and Its Application to Secure Communication
,” Neurocomputing
,
332
, pp. 29
–43
.10.1016/j.neucom.2018.11.02019.
Sun
,
J.
,
Liu
,
J.
,
Wang
,
Y. D.
,
Yu
,
Y.
, and
Sun
,
C. Y.
, 2020
, “
Fixed-Time Event-Triggered Synchronization of a Multilayer Kuramoto-Oscillator Network
,” Neurocomputing
,
379
, pp. 214
–226
.10.1016/j.neucom.2019.10.04020.
Li
,
Z. Y.
,
Xu
,
X.
,
Yan
,
T. R.
, and
Li
,
E.
, 2022
, “
Fixed-Time Synchronization in the Delayed Multiplex Networks by the Auxiliary-System Approach
,” Int. J. Control, Autom., Syst.
,
20
(7
), pp. 2169
–2177
.10.1007/s12555-021-0272-021.
Kilbas
,
A.
,
Srivastava
,
H.
, and
Trujillo
,
J.
, 2006
, Theory and Applications of Fractional Differential Equations
,
Elsevier
, Amsterdam, The Netherlands
.22.
Diethelm
,
K.
, 2010
, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type
,
Springer
, Berlin
.23.
Podlubny
,
I.
, 1999
, Fractional Differential Equations
,
Academic Press
,
San Diego, CA
.24.
Zhang
,
S.
,
Yu
,
Y.
, and
Wang
,
H.
, 2015
, “
Mittag-Leffler Stability of Fractional-Order Hopfield Neural Networks, Nonlinear Anal
,” Hybrid Syst.
,
16
, pp. 104
–121
.https://www.sciencedirect.com/science/article/abs/pii/S1751570X1400048X25.
Li
,
Y.
,
Chen
,
Y. Q.
, and
Podlubny
,
I.
, 2010
, “
Stability of Fractional-Order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag-Leffler Stability
,” Comput. Math. Appl.
,
59
(5
), pp. 1810
–1821
.10.1016/j.camwa.2009.08.01926.
Hardy
,
G.
,
Littlewood
,
J.
, and
Polya
,
G.
, 1951
, Inequalities
,
Cambridge University Press
,
London
.Copyright © 2023 by ASME
You do not currently have access to this content.