Inspired by time-delayed feedback control, it is shown that synchronization of non-identical systems can be achieved by mutual time-delayed feedback with an asymptotically vanishing interaction. An analytic perturbation scheme is developed, which uncovers the merits as well as the constraints of such an approach. As an application, the use of the concept for a secure communication channel is considered.
REFERENCES
1.
A.
Pikovsky
and J.
Kurths
, Synchronization: A Universal Concept in Nonlinear Sciences
(Cambridge University Press
, Cambridge
, 2003
).2.
Handbook of Chaos Control, 2nd ed., edited by E. Schöll and H. G. Schuster (Wiley-VCH, Weinheim, 2007).
3.
H.
Huijberts
, W.
Michiels
, and H.
Nijmeijer
, “Stabilizability via time-delayed feedback: An eigenvalue optimization approach
,” SIAM J. Appl. Dyn. Syst.
8
, 1
(2009
). 4.
G.
Stepan
, “Delay effects in the human sensory system during balancing
,” Philos. Trans. R. Soc. A
367
, 1195
(2009
). 5.
L. M.
Pecora
, F.
Sorrentino
, A. M.
Hagerstrom
, T. E.
Murphy
, and R.
Roy
, “Cluster synchronization and isolated desynchronization in complex networks with symmetries
,” Nat. Commun.
5
, 4079
(2014
). 6.
K.
Pyragas
, “Continuous control of chaos by self-controlling feedback
,” Phys. Lett. A
170
, 421
(1992
). 7.
A.
Amann
, E.
Schöll
, and W.
Just
, “Some basic remarks on eigenmode expansions of time-delay dynamics
,” Phys. A
373
, 191
(2007
). 8.
W.
Just
, E.
Reibold
, H.
Benner
, K.
Kacperski
, F.
Fronczak
, and J.
Hołyst
, “Limits of time-delayed feedback control
,” Phys. Lett. A
254
, 158
(1999
). 9.
B.
Fiedler
, V.
Flunkert
, M.
Georgi
, P.
Hövel
, and E.
Schöll
, “Refuting the odd number limitation of time-delayed feedback control
,” Phys. Rev. Lett.
98
, 114101
(2007
). 10.
J. K.
Hale
and S. M.
Verduyn Lunel
, Introduction to Functional Differential Equations
(Springer
, New York
, 1993
).11.
A.
Halanay
, Differential Equations: Stability, Oscillations, Time Lags
(Academic Press
, New York
, 1966
).12.
J.
Scheuer
and A.
Yariv
, “Giant fiber lasers: A new paradigm for secure key distribution
,” Phys. Rev. Lett.
97
, 140502
(2006
). 13.
H.
Nakajima
, “On analytical properties of delayed feedback control of chaos
,” Phys. Lett. A
232
, 207
(1997
). 14.
V.
Flunkert
, S.
Yanchuk
, T.
Dahms
, and E.
Schöll
, “Synchronizing distant nodes: A universal classification of networks
,” Phys. Rev. Lett.
105
, 254101
(2010
). © 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
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