Control of birhythmicity through conjugate self-feedback: Theory and experiment

Debabrata Biswas, Tanmoy Banerjee, Jürgen Kurths

Research output: Contribution to journalArticle

16 Citations (Scopus)
4 Downloads (Pure)

Abstract

Birhythmicity arises in several physical, biological, and chemical systems. Although many control schemes have been proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the control of birhythmic oscillation by introducing a self-feedback mechanism that incorporates the variable to be controlled and its canonical conjugate. Using a detailed analytical treatment, bifurcation analysis, and experimental demonstrations, we establish that the proposed technique is capable of eliminating birhythmicity and generates monorhythmic oscillation. Further, the detailed parameter space study reveals that, apart from monorhythmicity, the system shows a transition between birhythmicity and other dynamical forms of bistability. This study may have practical applications in controlling birhythmic behavior of several systems, in particular in biochemical and mechanical processes.
Original languageEnglish
Article number042226
Pages (from-to)1-7
Number of pages7
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume94
Issue number4
DOIs
Publication statusPublished - 31 Oct 2016

Fingerprint

oscillations
Oscillation
Experiment
Multistability
Bistability
Bifurcation Analysis
Parameter Space
Form

Cite this

Control of birhythmicity through conjugate self-feedback : Theory and experiment. / Biswas, Debabrata; Banerjee, Tanmoy; Kurths, Jürgen.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 94, No. 4, 042226, 31.10.2016, p. 1-7.

Research output: Contribution to journalArticle

@article{a0077b7296ca4554be3a80dfc7ad2c28,
title = "Control of birhythmicity through conjugate self-feedback: Theory and experiment",
abstract = "Birhythmicity arises in several physical, biological, and chemical systems. Although many control schemes have been proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the control of birhythmic oscillation by introducing a self-feedback mechanism that incorporates the variable to be controlled and its canonical conjugate. Using a detailed analytical treatment, bifurcation analysis, and experimental demonstrations, we establish that the proposed technique is capable of eliminating birhythmicity and generates monorhythmic oscillation. Further, the detailed parameter space study reveals that, apart from monorhythmicity, the system shows a transition between birhythmicity and other dynamical forms of bistability. This study may have practical applications in controlling birhythmic behavior of several systems, in particular in biochemical and mechanical processes.",
author = "Debabrata Biswas and Tanmoy Banerjee and J{\"u}rgen Kurths",
note = "ACKNOWLEDGMENTS D.B. acknowledges the financial support from CSIR, New Delhi, India, T.B. acknowledges the financial support from SERB, Department of Science and Technol- ogy (DST), India [Project Grant No.: SB/FTP/PS-005/2013]",
year = "2016",
month = "10",
day = "31",
doi = "10.1103/PhysRevE.94.042226",
language = "English",
volume = "94",
pages = "1--7",
journal = "Physical Review. E, Statistical, Nonlinear and Soft Matter Physics",
issn = "1539-3755",
publisher = "AMER PHYSICAL SOC",
number = "4",

}

TY - JOUR

T1 - Control of birhythmicity through conjugate self-feedback

T2 - Theory and experiment

AU - Biswas, Debabrata

AU - Banerjee, Tanmoy

AU - Kurths, Jürgen

N1 - ACKNOWLEDGMENTS D.B. acknowledges the financial support from CSIR, New Delhi, India, T.B. acknowledges the financial support from SERB, Department of Science and Technol- ogy (DST), India [Project Grant No.: SB/FTP/PS-005/2013]

PY - 2016/10/31

Y1 - 2016/10/31

N2 - Birhythmicity arises in several physical, biological, and chemical systems. Although many control schemes have been proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the control of birhythmic oscillation by introducing a self-feedback mechanism that incorporates the variable to be controlled and its canonical conjugate. Using a detailed analytical treatment, bifurcation analysis, and experimental demonstrations, we establish that the proposed technique is capable of eliminating birhythmicity and generates monorhythmic oscillation. Further, the detailed parameter space study reveals that, apart from monorhythmicity, the system shows a transition between birhythmicity and other dynamical forms of bistability. This study may have practical applications in controlling birhythmic behavior of several systems, in particular in biochemical and mechanical processes.

AB - Birhythmicity arises in several physical, biological, and chemical systems. Although many control schemes have been proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the control of birhythmic oscillation by introducing a self-feedback mechanism that incorporates the variable to be controlled and its canonical conjugate. Using a detailed analytical treatment, bifurcation analysis, and experimental demonstrations, we establish that the proposed technique is capable of eliminating birhythmicity and generates monorhythmic oscillation. Further, the detailed parameter space study reveals that, apart from monorhythmicity, the system shows a transition between birhythmicity and other dynamical forms of bistability. This study may have practical applications in controlling birhythmic behavior of several systems, in particular in biochemical and mechanical processes.

U2 - 10.1103/PhysRevE.94.042226

DO - 10.1103/PhysRevE.94.042226

M3 - Article

VL - 94

SP - 1

EP - 7

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 4

M1 - 042226

ER -