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.
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Research Article|
May 14 2019
Entrainment of aperiodic and periodic oscillations in the Mercury Beating Heart system using external periodic forcing
Pawan Kumar;
Pawan Kumar
1
Department of Physics, Indian Institute of Technology Bombay
, Powai, Mumbai 400 076, India
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P. Parmananda
;
P. Parmananda
1
Department of Physics, Indian Institute of Technology Bombay
, Powai, Mumbai 400 076, India
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Dinesh Kumar Verma;
Dinesh Kumar Verma
2
Centro de Investigación en Ciencias - (IICBA), UAEM
, Avenida Universidad 1001, Colonia Chamilpa, Cuernavaca, 62209 Morelos, Mexico
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Tanu Singla;
Tanu Singla
2
Centro de Investigación en Ciencias - (IICBA), UAEM
, Avenida Universidad 1001, Colonia Chamilpa, Cuernavaca, 62209 Morelos, Mexico
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Iram de Nicolás;
Iram de Nicolás
2
Centro de Investigación en Ciencias - (IICBA), UAEM
, Avenida Universidad 1001, Colonia Chamilpa, Cuernavaca, 62209 Morelos, Mexico
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J. Escalona
;
J. Escalona
2
Centro de Investigación en Ciencias - (IICBA), UAEM
, Avenida Universidad 1001, Colonia Chamilpa, Cuernavaca, 62209 Morelos, Mexico
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M. Rivera
M. Rivera
2
Centro de Investigación en Ciencias - (IICBA), UAEM
, Avenida Universidad 1001, Colonia Chamilpa, Cuernavaca, 62209 Morelos, Mexico
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Pawan Kumar
1
P. Parmananda
1
Dinesh Kumar Verma
2
Tanu Singla
2
Iram de Nicolás
2
J. Escalona
2
M. Rivera
2
1
Department of Physics, Indian Institute of Technology Bombay
, Powai, Mumbai 400 076, India
2
Centro de Investigación en Ciencias - (IICBA), UAEM
, Avenida Universidad 1001, Colonia Chamilpa, Cuernavaca, 62209 Morelos, Mexico
Note: This paper is part of the Focus Issue, “Nonlinear Chemical Dynamics and Its Interdisciplinary Impact: Dedicated to Ken Showalter on the Occasion of his 70th Birthday.”
Chaos 29, 053112 (2019)
Article history
Received:
November 29 2018
Accepted:
April 25 2019
Citation
Pawan Kumar, P. Parmananda, Dinesh Kumar Verma, Tanu Singla, Iram de Nicolás, J. Escalona, M. Rivera; Entrainment of aperiodic and periodic oscillations in the Mercury Beating Heart system using external periodic forcing. Chaos 1 May 2019; 29 (5): 053112. https://doi.org/10.1063/1.5083179
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