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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

Special Collection: Nonlinear Chemical Dynamics and Its Interdisciplinary Impact: Dedicated to Ken Showalter on the Occasion of his 70th Birthday

Pawan Kumar;

Pawan Kumar

1

Department of Physics, Indian Institute of Technology Bombay

, Powai, Mumbai 400 076,

India

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P. Parmananda

0000-0001-5410-5148

;

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

0000-0001-8620-3762

;

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

0000-0002-9952-2823

M. Rivera

2

Centro de Investigación en Ciencias - (IICBA), UAEM

, Avenida Universidad 1001, Colonia Chamilpa, Cuernavaca, 62209 Morelos,

Mexico

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Author & Article Information

Pawan Kumar ¹

,

P. Parmananda

^{^{https://orcid.org/0000-0001-5410-5148}}

¹

,

Dinesh Kumar Verma ²

,

Tanu Singla ²

,

Iram de Nicolás ²

,

J. Escalona

^{^{https://orcid.org/0000-0001-8620-3762}}

²

,

M. Rivera

^{^{https://orcid.org/0000-0002-9952-2823}}

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)

https://doi.org/10.1063/1.5083179

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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© 2019 Author(s).

2019

Author(s)

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