This paper examines synchronization of a set of metronomes placed on a lightweight foam platform. Two configurations of the set of metronomes are considered: a row setup containing one-dimensional coupling and a cross setup containing two-dimensional coupling. Depending on the configuration and coupling between the metronomes, i.e., the platform parameters, in- and/or anti-phase synchronized behavior is observed in the experiments. To explain this behavior, mathematical models of a metronome and experimental setups have been derived and used in a local stability analysis. It is numerically and experimentally demonstrated that varying the coupling parameters for both configurations has a significant influence on the stability of the synchronized solutions.

1.
Aton
,
S. J.
and
Herzog
,
E. D.
, “
Come together, right now: Synchronization of rhythms in a mammalian circadian clock
,”
Neuron
48
,
531
534
(
2005
).
2.
Bennett
,
M.
,
Schatz
,
M. F.
,
Rockwood
,
H.
, and
Wiesenfeld
,
K.
, “
Huygens's clocks
,”
Proc. R. Soc. A
458
,
563
579
(
2002
).
3.
Czolczynski
,
K.
,
Perlikowski
,
P.
,
Stefanski
,
A.
, and
Kapitaniak
,
T.
, “
Clustering and synchronization of n Huygens clocks
,”
Physica A
388
,
5013
5023
(
2009
).
4.
Czolczynski
,
K.
,
Perlikowski
,
P.
,
Stefanski
,
A.
, and
Kapitaniak
,
T.
, “
Huygens' odd sympathy experiment revisited
,”
Int. J. Bifurcation Chaos
21
,
2047
2056
(
2011
).
5.
Doedel
,
E. J.
and
Oldeman
,
B. E.
, Auto-07p: Continuation and bifurcation software,
2012
.
6.
Gardner
,
F. M.
,
Phaselock Techniques
(
John Wiley & Sons
,
2005
).
7.
Hoogeboom
,
F.
,
Pogromsky
,
A.
, and
Nijmeijer
,
H.
, “
Huygens synchronization: Experiments, modeling, and local stability analysis
,” in
Proceedings of the 4th IFAC Conference on Analysis and Control of Chaotic Systems
(
2015
).
8.
Huygens
,
C.
,
Oeuvres Complètes
(
Swets & Zeitlinger BV
,
Amsterdam
,
1967
), Vol.
17
, pp.
156
189
.
9.
Ikeguchi
,
T.
, Ikeguchi Laboratory, Saitama University,
2014
.
10.
Jovanovic
,
V.
and
Koshkin
,
S.
, “
Synchronization of huygens' clocks and the poincaré method
,”
J. Sound Vib.
331
,
2887
2900
(
2012
).
11.
Kapitaniak
,
M.
,
Czolczynski
,
K.
,
Perlikowski
,
P.
,
Stefanski
,
A.
, and
Kapitaniak
,
T.
, “
Synchronization of clocks
,”
Phys. Rep.
517
,
1
69
(
2012
).
12.
Koluda
,
P.
,
Perlikowski
,
P.
,
Czolczynski
,
K.
, and
Kapitaniak
,
T.
, “
Synchronization of two self-excited double pendula
,”
Eur. Phys. J. Spec. Top.
223
,
613
629
(
2014
).
13.
Kuznetsov
,
N. V.
,
Leonov
,
G. A.
,
Nijmeijer
,
H.
, and
Pogromsky
,
A.
, “
Synchronization of two metronomes
,” in
Proceedings of the 3rd IFAC Workshop on Periodic Control Systems
(
2007
).
14.
Leonov
,
G. A.
,
Kuznetsov
,
N. V.
,
Yuldashev
,
M. V.
, and
Yuldashev
,
R. V.
, “
Hold-in, pull-in, and lock-in ranges of pll circuits: Rigorous mathematical definitions and limitations of classical theory
,”
IEEE Trans. Circuits Syst. I
62
,
2454
2464
(
2015
).
15.
Néda
,
Z.
,
Ravasz
,
E.
,
Brechet
,
Y.
,
Vicsek
,
T.
, and
Barabási
,
A.-L.
, “
Self-organizing processes: The sound of many hands clapping
,”
Nature
403
,
849
850
(
2000
).
16.
Nomura
,
K.
,
Takei
,
Y.
, and
Yanagida
,
Y.
, “
Comparison of cardio-locomotor synchronization during running and cycling
,”
Eur. J. Appl. Phys.
89
,
221
229
(
2003
).
17.
Oud
,
W.
,
Nijmeijer
,
H.
, and
Pogromsky
,
A. Y.
, “
A study of Huijgens' synchronization: experimental results
,”
Group Coordination and Cooperative Control
(
Springer
,
2006
), pp.
191
203
.
18.
Pantaleone
,
J.
, “
Synchronization of metronomes
,”
Am. J. Phys.
70
,
992
1000
(
2002
).
19.
Peña Ramirez
,
J.
,
Aihara
,
K.
,
Fey
,
R.
, and
Nijmeijer
,
H.
, “
Further understanding of Huygens coupled clocks: The effect of stiffness
,”
Physica D
270
,
11
19
(
2014a
).
20.
Peña Ramirez
,
J.
,
Alberto Olvera
,
L.
,
Nijmeijer
,
H.
, and
Alvarez
,
J.
, “
The sympathy of two pendulum clocks: Beyond Huygens' observations
,”
Sci. Rep.
6
,
23580
(
2016
).
21.
Peña Ramirez
,
J.
,
Fey
,
R.
,
Aihara
,
K.
, and
Nijmeijer
,
H.
, “
An improved model for the classical Huygens' experiment on synchronization of pendulum clocks
,”
J. Sound Vib.
333
,
7248
7266
(
2014b
).
22.
Pikovsky
,
A.
,
Rosenblum
,
M.
, and
Kurths
,
J.
,
Synchronization: A Universal Concept in Nonlinear Sciences
(
Cambridge University Press
,
2003
), Vol.
12
.
23.
Strogatz
,
S.
,
Sync: The Emerging Science of Spontaneous Order
(
Hyperion
,
2003
).
24.
Thomson
,
A.
,
Time and Timekeepers
(
T&W Boone
,
1842
).
You do not currently have access to this content.