This paper mainly investigates the anti-phase synchronization of two coupled mechanical metronomes not only by means of numerical simulations, but also by experimental tests. It is found that the attractor basin of anti-phase synchronization enlarges as the rolling friction increases. Furthermore, this paper studies the relationship between different initial conditions and synchronization types. The impacts of rolling friction on in-phase and anti-phase synchronization times are also discovered. Finally, in-phase and anti-phase synchronization conditions of non-identical metronomes are discussed. These results indicate the potential complexity of the dynamics of coupled metronomes.
REFERENCES
1.
S.
Boccaletti
, J.
Kurths
, G.
Osipov
, D. L.
Valladares
, and C. S.
Zhou
, Phys. Rep.
366
, 1
(2002
).2.
M.
Bennett
, M. F.
Schatz
, H.
Rockwood
, and K.
Wiesenfeld
, Proc. R. Soc. London, Ser. A
458
, 563
(2002
).3.
K.
Wiesenfeld
, P.
Colet
, and S. H.
Strogatz
, Phys. Rev. Lett.
76
, 404
(1996
).4.
M. C.
Cross
, A.
Zumdieck
, R.
Lifshitz
, and J. L.
Rogers
, Phys. Rev. Lett.
93
, 224101
(2004
).5.
B.
Ermentrout
, J. Math. Biol.
29
, 571
(1991
).6.
P. A.
Tass
, Europhys. Lett.
53
, 15
(2001
).7.
P. A.
Tass
, Biol. Cybern.
87
, 102
(2002
).8.
H.
Hong
and S. H.
Strogatz
, Phys. Rev. Lett.
106
, 054102
(2011
).9.
D.
Taylor
, E.
Ott
, and J. G.
Restrepo
, Phys. Rev. E
81
, 046214
(2010
).10.
A.
Arenas
, A.
Díaz-Guilera
, J.
Kurths
, Y.
Moreno
, and C.
Zhou
, Phys. Rep.
469
, 93
(2008
).11.
J.
Pantaleone
, Am. J. Phys.
70
, 992
(2002
).12.
M.
Senator
, J. Sound Vib.
291
, 566
(2006
).13.
A. L.
Fradkov
and B.
Andrievsky
, Int. J. Non-linear Mech.
42
, 895
(2007
).14.
R.
Dilao
, Chaos
19
, 023118
(2009
).15.
H.
Ulrichs
, A.
Mann
, and U.
Parlitz
, Chaos
19
, 043120
(2009
).16.
K.
Czolczynski
, P.
Perlikowski
, A.
Stefanski
, and T.
Kapitaniak
, Phys. A
388
, 5013
(2009
).17.
K.
Czolczynski
, P.
Perlikowski
, A.
Stefanski
, and T.
Kapitaniak
, Prog. Theor. Phys.
122
, 1027
(2009
).18.
K.
Czolczynski
, P.
Perlikowski
, A.
Stefanski
, and T.
Kapitaniak
, Chaos
21
, 023129
(2011
).19.
P.
Perlikowski
, M.
Kapitaniak
, K.
Czolczynski
, A.
Stefanski
, and T.
Kapitaniak
, “Chaos in coupled clocks
,” Int. J. Bifurcation Chaos
(unpublished).20.
G.
Yi
, H. K.
Lee
, S. H.
Jeon
, and B. J.
Kim
, Int. J. Bifurcation Chaos
20
, 2179
(2010
).21.
A. S. K.
Czolczynski
, P.
Perlikowski
, and T.
Kapitaniak
, Int. J. Bifurcation Chaos
21
, 7
(2011
).© 2012 American Institute of Physics.
2012
American Institute of Physics
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