Coupled oscillatory systems are good models that are able to describe a variety of higher dimensional nonlinear phenomena. Coupled chaotic circuits produce many kinds of interesting synchronization phenomena. In recent years, research studies on complex networks related to the synchronization of coupled oscillators have attracted much attention. In the real world, there are a variety of different network structures. We focus on the competitive interaction network that includes conflict between two networks. Here, we propose a new paradigm for this competitive interaction network using coupled chaotic circuits.
REFERENCES
1
J. D.
Watts
and S. H.
Strogatz
, “Collective dynamics of small-world networks
,” Nature
393
, 440
(1998
). 2
S. H.
Strogatz
, “Exploring complex networks
,” Nature
410
, 268
(2001
). 3
E.
Bullmore
and O.
Sporns
, “The economy of brain network organization
,” Nat. Rev. Neurosci.
10
, 186
(2009
). 4
T.
Nishikawa
, A. E.
Motter
, Y. C.
Lai
, and F. C.
Hoppensteadt
, “Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
,” Phys. Rev. Lett.
91
, 014101
(2003
). 5
Y.
Moreno
and A. F.
Pacheco
, “Synchronization of Kuramoto oscillators in scale-free networks
,” Europhys. Lett.
68
, 603
(2004
). 6
M.
Chavez
, D.-U.
Hwang
, A.
Amann
, H. G. E.
Hentschel
, and S.
Boccaletti
, “Synchronization is enhanced in weighted complex networks
,” Phys. Rev. Lett.
94
, 218701
(2005
). 7
A.
Arenas
, A.
Díaz-Guilera
, and C. J.
Perez-Vicente
, “Synchronization reveals topological scales in complex networks
,” Phys. Rev. Lett.
96
, 114102
(2006
). 8
C.
Zhou
, A. E.
Motter
, and J.
Kurths
, “Universality in the synchronization of weighted random networks
,” Phys. Rev. Lett.
96
, 034101
(2006
). 9
J.
Gómez-Gardeñes
, Y.
Moreno
, and A.
Arenas
, “Paths to synchronization in complex networks
,” Phys. Rev. Lett.
98
, 034101
(2007
). 10
I.
Lodato
, S.
Boccaletti
, and V.
Latora
, “Synchronization properties of network motifs
,” Europhys. Lett.
78
, 28001
(2007
). 11
A.
Arenas
, A.
Díaz-Guilera
, J.
Kurths
, Y.
Moreno
, and C.
Zhou
, “Synchronization in complex networks
,” Phys. Rep.
469
, 93
(2008
). 12
J.
Gómez-Gardeñes
, S.
Gomez
, A.
Arenas
, and Y.
Moreno
, “Explosive synchronization transitions in scale-free networks
,” Phys. Rev. Lett.
106
, 128701
(2011
). 13
L. V.
Gambuzza
, A.
Cardillo
, A.
Fiasconaro
, L.
Fortuna
, J.
Gomez-Gardenes
, and M.
Frasca
, “Analysis of remote synchronization in complex networks
,” Chaos
23
, 043103
(2013
). 14
S.
Boccaletti
, J.
Kurths
, G.
Osipov
, D.
Valladares
, and C.
Zhou
, “The synchronization of chaotic systems
,” Phys. Rep.
366
, 1
–101
(2002
). 15
A.
Arenas
, A.
Diaz-Guilera
, J.
Kurths
, Y.
Moreno
, and C.
Zhou
, “Phase synchronization of chaotic oscillators
,” Phys. Rep.
469
, 93
–153
(2008
). 16
K.
Ago
, Y.
Uwate
, and Y.
Nishio
, “Influence of local bridge on a complex network of coupled chaotic circuits,” in Proceedings of International Symposium on Nonlinear Theory and its Applications (NOLTA’14) (IEICE
, 2014
), pp. 731–734. 17
K.
Oi
, Y.
Uwate
, and Y.
Nishio
, “Synchronization and clustering in coupled parametrically excited oscillators with small mismatch,” in Proceedings of ISCAS’15 (IEEE
, 2015
), pp. 910–913.18
T.
Chikazawa
, Y.
Uwate
, and Y.
Nishio
, “Chaos propagation in coupled chaotic circuits with multi-ring combination,” in Proceedings of APCCAS’16 (IEEE
, 2016
), pp. 65–68.19
Y.
Uwate
and Y.
Nishio
, “Synchronization in dynamical oscillatory networks with non-uniform coupling distributions,” in Proceedings of ISCAS’17 (IEEE
, 2017
), pp. 846–849.20
A.
Giron
, H.
Saiz
, F. S.
Bacelar
, R. F. S.
Andrade
, and J.
Gomez-Gardenes
, “Synchronization unveils the organization of ecological network with positive and negative interactions
,” Chaos
26
(6
), 065302
(2016
). 21
J.
Garland
, A. M.
Berdahl
, J.
Sun
, and E. M.
Bollt
, “Anatomy of leadership in collective behaviour
,” Chaos
28
(7
), 075308
(2018
). 22
Y.
Uwate
, Y.
Takamaru
, T.
Ott
, and Y.
Nishio
, “Clustering using chaotic circuit networks with weighted couplings
,” Int. J. Bifurcat. Chaos
29
(4
), 1950053
(2019
). 23
X.
Li
and G.
Chen
, “Synchronization and desynchronization of complex dynamical networks: An engineering viewpoint
,” IEEE Trans. Circuits Syst. I Fundam. Theory Appl.
50
(11
), 1381
–1390
(2003
). 24
C.
Liu
, Q.
Chen
, and J.
Zhang
, “Coupled Van Der Pol oscillators utilised as central pattern generators for quadruped locomotion,” in Proceedings of CCDC’09 (IEEE
, 2009
), pp. 3677–3682.25
S.
Mondal
, A.
Nandy
, Chandrapal
, P.
Chakraborty
, and G. C.
Nandi
, “A central pattern generator based nonlinear controller to simulate biped locomotion with a stable human gait oscillation
,” Int. J. Robot. Autom.
2
(2
), 93
–106
(2011
).26
M.
Shinriki
, M.
Yamamoto
, and S.
Mori
, “Multimode oscillations in a modified Van Der Pol oscillator containing a positive nonlinear conductance
,” Proc. IEEE
69
, 394
–395
(1981
). © 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.