Basin of attraction for chimera states in a network of Rossler oscillators

Vagner dos Santos; Fernando S. Borges; Kelly C. Iarosz; Ibere L. Caldas; J. D. Szezech; Ricardo L. Viana; Murilo S. Baptista; Antonio M. Batista

doi:10.1063/5.0014013

Basin of attraction for chimera states in a network of Rossler oscillators

Vagner dos Santos^*, Fernando S. Borges, Kelly C. Iarosz, Ibere L. Caldas, J. D. Szezech, Ricardo L. Viana, Murilo S. Baptista, Antonio M. Batista

^*Corresponding author for this work

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

14 Citations (Scopus)

Abstract

Chimera states are spatiotemporal patterns in which coherent and incoherent dynamics coexist simultaneously. These patterns were observed in both locally and nonlocally coupled oscillators. We study the existence of chimera states in networks of coupled Rossler oscillators. The Rossler oscillator can exhibit periodic or chaotic behavior depending on the control parameters. In this work, we show that the existence of coherent, incoherent, and chimera states depends not only on the coupling strength, but also on the initial state of the network. The initial states can belong to complex basins of attraction that are not homogeneously distributed. Due to this fact, we characterize the basins by means of the uncertainty exponent and basin stability. In our simulations, we find basin boundaries with smooth, fractal, and riddled structures.

Original language	English
Article number	083115
Number of pages	8
Journal	Chaos
Volume	30
Issue number	8
Early online date	4 Aug 2020
DOIs	https://doi.org/10.1063/5.0014013
Publication status	Published - Aug 2020

Bibliographical note

ACKNOWLEDGMENTS: We wish to acknowledge the support: CNPq, CAPES, Fundação Araucária, and São Paulo Research Foundation (Process Nos. FAPESP 2015/07311-7, 2017/18977-1, and 2018/03211-6).

Data Availability Statement

DATA AVAILABILITY: The data that support the findings of this study are available from the corresponding author upon reasonable request.

Keywords

SYNCHRONIZATION
PHASE

Access to Document

10.1063/5.0014013Licence: Unspecified

Cite this

@article{6d4dc6a4324a471f8b880ab7b39979e9,

title = "Basin of attraction for chimera states in a network of Rossler oscillators",

abstract = "Chimera states are spatiotemporal patterns in which coherent and incoherent dynamics coexist simultaneously. These patterns were observed in both locally and nonlocally coupled oscillators. We study the existence of chimera states in networks of coupled Rossler oscillators. The Rossler oscillator can exhibit periodic or chaotic behavior depending on the control parameters. In this work, we show that the existence of coherent, incoherent, and chimera states depends not only on the coupling strength, but also on the initial state of the network. The initial states can belong to complex basins of attraction that are not homogeneously distributed. Due to this fact, we characterize the basins by means of the uncertainty exponent and basin stability. In our simulations, we find basin boundaries with smooth, fractal, and riddled structures.",

keywords = "SYNCHRONIZATION, PHASE",

author = "{dos Santos}, Vagner and Borges, {Fernando S.} and Iarosz, {Kelly C.} and Caldas, {Ibere L.} and Szezech, {J. D.} and Viana, {Ricardo L.} and Baptista, {Murilo S.} and Batista, {Antonio M.}",

note = "ACKNOWLEDGMENTS: We wish to acknowledge the support: CNPq, CAPES, Funda{\c c}{\~a}o Arauc{\'a}ria, and S{\~a}o Paulo Research Foundation (Process Nos. FAPESP 2015/07311-7, 2017/18977-1, and 2018/03211-6). ",

year = "2020",

month = aug,

doi = "10.1063/5.0014013",

language = "English",

volume = "30",

journal = "Chaos",

issn = "1054-1500",

publisher = "American Institute of Physics",

number = "8",

}

TY - JOUR

T1 - Basin of attraction for chimera states in a network of Rossler oscillators

AU - dos Santos, Vagner

AU - Borges, Fernando S.

AU - Iarosz, Kelly C.

AU - Caldas, Ibere L.

AU - Szezech, J. D.

AU - Viana, Ricardo L.

AU - Baptista, Murilo S.

AU - Batista, Antonio M.

N1 - ACKNOWLEDGMENTS: We wish to acknowledge the support: CNPq, CAPES, Fundação Araucária, and São Paulo Research Foundation (Process Nos. FAPESP 2015/07311-7, 2017/18977-1, and 2018/03211-6).

PY - 2020/8

Y1 - 2020/8

N2 - Chimera states are spatiotemporal patterns in which coherent and incoherent dynamics coexist simultaneously. These patterns were observed in both locally and nonlocally coupled oscillators. We study the existence of chimera states in networks of coupled Rossler oscillators. The Rossler oscillator can exhibit periodic or chaotic behavior depending on the control parameters. In this work, we show that the existence of coherent, incoherent, and chimera states depends not only on the coupling strength, but also on the initial state of the network. The initial states can belong to complex basins of attraction that are not homogeneously distributed. Due to this fact, we characterize the basins by means of the uncertainty exponent and basin stability. In our simulations, we find basin boundaries with smooth, fractal, and riddled structures.

AB - Chimera states are spatiotemporal patterns in which coherent and incoherent dynamics coexist simultaneously. These patterns were observed in both locally and nonlocally coupled oscillators. We study the existence of chimera states in networks of coupled Rossler oscillators. The Rossler oscillator can exhibit periodic or chaotic behavior depending on the control parameters. In this work, we show that the existence of coherent, incoherent, and chimera states depends not only on the coupling strength, but also on the initial state of the network. The initial states can belong to complex basins of attraction that are not homogeneously distributed. Due to this fact, we characterize the basins by means of the uncertainty exponent and basin stability. In our simulations, we find basin boundaries with smooth, fractal, and riddled structures.

KW - SYNCHRONIZATION

KW - PHASE

U2 - 10.1063/5.0014013

DO - 10.1063/5.0014013

M3 - Article

SN - 1054-1500

VL - 30

JO - Chaos

JF - Chaos

IS - 8

M1 - 083115

ER -

Basin of attraction for chimera states in a network of Rossler oscillators

Abstract

Bibliographical note

Data Availability Statement

Keywords

Access to Document

Fingerprint

Cite this