We report experimental results indicating entrainment of aperiodic and periodic oscillatory dynamics in the Mercury Beating Heart (MBH) system under the influence of superimposed periodic forcing. Aperiodic oscillations in MBH were controlled to generate stable topological modes, namely, circle, ellipse, and triangle, evolving in a periodic fashion at different parameters of the forcing signal. These periodic dynamics show 1:1 entrainment for circular and elliptical modes, and additionally the controlled system exhibits 1:2 entrainment for elliptical and triangular modes at a different set of parameters. The external periodic forcing of the periodic MBH system reveals the existence of domains of entrainment (1:1, 1:2, 1:3, and 1:4) represented in the Arnold tongue structures. Moreover, Devil’s staircase is obtained when the amplitude-frequency space of parameters of the applied signal is scanned.

1.
A.
Pikovsky
,
M.
Rosenblum
, and
J.
Kurths
,
Synchronization: A Universal Concept in Nonlinear Sciences
(
Cambridge University Press
,
Cambridge
,
2003
).
2.
C.
Hugenii
,
Horologium Oscillatorium
(
Apud F.
Muguet
,
Paris
,
1673
).
3.
W. J.
Yeh
,
D. R.
He
, and
Y. H.
Kao
,
Phys. Rev. Lett.
52
,
480
(
1984
).
4.
S.
Martin
and
W.
Martienssen
,
Phys. Rev. Lett.
56
,
1522
(
1986
).
5.
J.
Maurer
and
A.
Libchaber
,
J. Phys. (France) Lett.
40
,
419
(
1979
).
6.
R.
Makki
,
A. P.
Muñuzuri
, and
J.
Perez-Mercader
,
Chem. Eur. J.
20
,
14213
14217
(
2014
).
7.
M.
Pagitsas
,
D.
Sazou
,
A.
Karantonis
, and
C.
Georgolios
,
J. Electroanal. Chem.
327
,
93
(
1992
).
8.
F.
Montoya
,
M.
Rivera
,
J.
Escalona
, and
P.
Parmananda
,
Phys. Lett. A
377
(
43
),
3124
(
2013
).
10.
A.
Pikovsky
,
M.
Zaks
,
M.
Rosenblum
,
G.
Osipov
, and
J.
Kurths
,
Chaos
7
,
680
(
1997
).
12.
P.
Parmananda
,
M.
Rivera
,
R.
Madrigal
,
I. Z.
Kiss
, and
V.
Gáspár
,
J. Phys. Chem. B
104
(
49
),
11748
(
2000
).
13.
M.
Rivera
,
P.
Parmananda
, and
M.
Eiswirth
,
Phys. Rev. E
65
,
025201(R)
(
2002
).
14.
P.
Parmananda
,
H.
Mahara
,
T.
Amemiya
, and
T.
Yamaguchi
,
Phys. Rev. Lett.
87
,
238302
(
2001
).
15.
H.
Mahara
,
T.
Yamaguchi
,
Y.
Morikawa
,
T.
Amemiya
,
T.
Yamamoto
,
H.
Miike
, and
P.
Parmananda
,
Physica D
205
,
275
(
2005
).
16.
T. R.
Chigwada
,
P.
Parmananda
, and
K.
Showalter
,
Phys. Rev. Lett.
96
,
244101
(
2006
).
17.
D.
Avnir
,
J. Chem. Educ.
66
,
211
(
1989
).
18.
J.
Keizer
,
P. A.
Rock
, and
S. W.
Lin
,
J. Am. Chem. Soc.
101
,
5637
(
1979
).
19.
S.
Castillo-Rojas
,
J. L.
Gonzalez-Chavez
,
L.
Vicente
, and
G.
Burillo
,
J. Phys. Chem. A
105
,
8038
(
2001
).
20.
P.
Kumar
and
P.
Parmananda
,
Chaos
28
(
4
),
045105
(
2018
).
21.
S.
Smolin
and
R.
Imbihl
,
J. Phys. Chem.
100
(
49
),
19055
(
1996
).
22.
J.
Olson
,
C.
Ursenbach
,
V. I.
Birss
, and
W. G.
Laidlaw
,
J. Phys. Chem.
93
(
25
),
8258
(
1989
).
23.
D. K.
Verma
,
A. Q.
Contractor
, and
P.
Parmananda
,
J. Phys. Chem. A
117
(
2
),
267
(
2013
).
24.
E.
Ramírez-Álvarez
,
J. L.
Ocampo-Espindola
,
F.
Montoya
,
F.
Yousif
,
F.
Vázquez
, and
M.
Rivera
,
J. Phys. Chem. A
118
(
45
),
10673
(
2014
).
25.
D. K.
Verma
,
H.
Singh
,
P.
Parmananda
,
A. Q.
Contractor
, and
M.
Rivera
,
Chaos
25
(
6
),
064609
(
2015
).
26.
D. K.
Verma
,
H.
Singh
,
A. Q.
Contractor
, and
P.
Parmananda
,
J. Phys. Chem. A
118
(
26
),
4647
(
2014
).
27.
P.
Kumar
,
D. K.
Verma
,
P.
Parmananda
, and
S.
Boccaletti
,
Phys. Rev. E
91
,
062909
(
2015
).
You do not currently have access to this content.