Characterization in bi-parameter space of a non-ideal oscillator

S. L. T. de Souza; A. M. Batista; M. S. Baptista; I. L. Caldas; J. M. Balthazar

doi:10.1016/j.physa.2016.09.020

Characterization in bi-parameter space of a non-ideal oscillator

S. L. T. de Souza
, A. M. Batista
, M. S. Baptista
, I. L. Caldas
, J. M. Balthazar

Universidade Federal de São João del-Rei
Universidade de São Paulo
Universidade Estadual de Ponta Grossa
Instituto Tecnológico de Aeronáutica

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

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Abstract

We investigate the dynamical behavior of a non-ideal Duffing oscillator, a system composed of a mass–spring–pendulum driven by a DC motor with limited power supply. To identify new features on Duffing oscillator parameter space due to the limited power supply, we provide an extensive numerical characterization in the bi-parameter space by using Lyapunov exponents. Following this procedure, we identify remarkable new organized distribution of periodic windows, the ones known as Arnold tongues and also shrimp-shaped structures. In addition, we also identify intertwined basins of attraction for coexisting multiple attractors connected with tongues.

Original language	English
Pages (from-to)	224-231
Number of pages	8
Journal	Physica. A, Statistical Mechanics and its Applications
Volume	466
Early online date	21 Sept 2016
DOIs	https://doi.org/10.1016/j.physa.2016.09.020
Publication status	Published - 15 Jan 2017

Bibliographical note

The authors thank scientific agencies CAPES, CNPq (112952/2015-1), and FAPESP (2011/ 19269-11). M. S. Baptista also thanks EPSRC (EP/I03 2606/1).

Keywords

chaos
Arnold tongues
shrimp-shaped structures
coupled oscillators

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10.1016/j.physa.2016.09.020

Accepted Manuscript
© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 10.3 MBLicence: CC BY-NC-ND

Cite this

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title = "Characterization in bi-parameter space of a non-ideal oscillator",

abstract = "We investigate the dynamical behavior of a non-ideal Duffing oscillator, a system composed of a mass{\textendash}spring{\textendash}pendulum driven by a DC motor with limited power supply. To identify new features on Duffing oscillator parameter space due to the limited power supply, we provide an extensive numerical characterization in the bi-parameter space by using Lyapunov exponents. Following this procedure, we identify remarkable new organized distribution of periodic windows, the ones known as Arnold tongues and also shrimp-shaped structures. In addition, we also identify intertwined basins of attraction for coexisting multiple attractors connected with tongues.",

keywords = "chaos, Arnold tongues, shrimp-shaped structures, coupled oscillators",

author = "\{de Souza\}, \{S. L. T.\} and Batista, \{A. M.\} and Baptista, \{M. S.\} and Caldas, \{I. L.\} and Balthazar, \{J. M.\}",

note = "The authors thank scientific agencies CAPES, CNPq (112952/2015-1), and FAPESP (2011/ 19269-11). M. S. Baptista also thanks EPSRC (EP/I03 2606/1). ",

year = "2017",

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doi = "10.1016/j.physa.2016.09.020",

language = "English",

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journal = "Physica. A, Statistical Mechanics and its Applications",

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T1 - Characterization in bi-parameter space of a non-ideal oscillator

AU - de Souza, S. L. T.

AU - Batista, A. M.

AU - Baptista, M. S.

AU - Caldas, I. L.

AU - Balthazar, J. M.

N1 - The authors thank scientific agencies CAPES, CNPq (112952/2015-1), and FAPESP (2011/ 19269-11). M. S. Baptista also thanks EPSRC (EP/I03 2606/1).

PY - 2017/1/15

Y1 - 2017/1/15

N2 - We investigate the dynamical behavior of a non-ideal Duffing oscillator, a system composed of a mass–spring–pendulum driven by a DC motor with limited power supply. To identify new features on Duffing oscillator parameter space due to the limited power supply, we provide an extensive numerical characterization in the bi-parameter space by using Lyapunov exponents. Following this procedure, we identify remarkable new organized distribution of periodic windows, the ones known as Arnold tongues and also shrimp-shaped structures. In addition, we also identify intertwined basins of attraction for coexisting multiple attractors connected with tongues.

AB - We investigate the dynamical behavior of a non-ideal Duffing oscillator, a system composed of a mass–spring–pendulum driven by a DC motor with limited power supply. To identify new features on Duffing oscillator parameter space due to the limited power supply, we provide an extensive numerical characterization in the bi-parameter space by using Lyapunov exponents. Following this procedure, we identify remarkable new organized distribution of periodic windows, the ones known as Arnold tongues and also shrimp-shaped structures. In addition, we also identify intertwined basins of attraction for coexisting multiple attractors connected with tongues.

KW - chaos

KW - Arnold tongues

KW - shrimp-shaped structures

KW - coupled oscillators

U2 - 10.1016/j.physa.2016.09.020

DO - 10.1016/j.physa.2016.09.020

M3 - Article

SN - 0378-4371

VL - 466

SP - 224

EP - 231

JO - Physica. A, Statistical Mechanics and its Applications

JF - Physica. A, Statistical Mechanics and its Applications

ER -

Characterization in bi-parameter space of a non-ideal oscillator

Abstract

Bibliographical note

Keywords

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