Riddling: Chimera’s dilemma

V. Santos; J. D. Szezech Jr; A. M. Batista; K. C. Iarosz; M. S. Baptista; H. P. Ren; C. Grebogi; R. L. Viana; I. L. Caldas; Y. L. Maistrenko; J. Kurths

doi:10.1063/1.5048595

Riddling: Chimera’s dilemma

V. Santos, J. D. Szezech Jr, A. M. Batista, K. C. Iarosz, M. S. Baptista, H. P. Ren, C. Grebogi, R. L. Viana, I. L. Caldas, Y. L. Maistrenko, J. Kurths

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Abstract

We investigate the basin of attraction properties and its boundaries for chimera states in a circulant network of Hénon maps. It is known that coexisting basins of attraction lead to a hysteretic behaviour in the diagrams of the density of states as a function of a varying parameter. Chimera states, for which coherent and incoherent domains occur simultaneously, emerge as a consequence of the coexistence of basin of attractions for each state. Consequently, the distribution of chimera states can remain invariant by a parameter change, and it can also suffer subtle changes when one of the basins ceases to exist. A similar phenomenon is observed when perturbations are applied in the initial conditions. By means of the uncertainty exponent, we characterise the basin boundaries between the coherent and chimera states, and between the incoherent and chimera states. This way, we show that the density of chimera states can be not only moderately sensitive but also highly sensitive to initial conditions. This chimera’s dilemma is a consequence of the fractal and riddled nature of the basin boundaries.

Original language	English
Article number	081105
Number of pages	6
Journal	Chaos
Volume	28
Issue number	8
Early online date	23 Aug 2018
DOIs	https://doi.org/10.1063/1.5048595
Publication status	Published - Aug 2018

Bibliographical note

We wish to acknowledge the support: Sao Paulo Research Foundation (FAPESP) under Grants 2011/19296-1, 2015/05186-0, 2015/07311-7, 2015/50122-0, and
2017/20920-8, Conselho Nacional de Desenvolvimento Cientıfico e Tecnologico (CNPq), and Coordena¸cao de Aperfei¸coamento de Pessoal de Nıvel Superior (CAPES).

Keywords

nlin.CD

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Riddling: Chimera's dilemma
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Chaos. 2018 Aug;28(8). 081105. and may be found at https://doi.org/10.1063/1.5048595.
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title = "Riddling: Chimera{\textquoteright}s dilemma ",

abstract = "We investigate the basin of attraction properties and its boundaries for chimera states in a circulant network of H{\'e}non maps. It is known that coexisting basins of attraction lead to a hysteretic behaviour in the diagrams of the density of states as a function of a varying parameter. Chimera states, for which coherent and incoherent domains occur simultaneously, emerge as a consequence of the coexistence of basin of attractions for each state. Consequently, the distribution of chimera states can remain invariant by a parameter change, and it can also suffer subtle changes when one of the basins ceases to exist. A similar phenomenon is observed when perturbations are applied in the initial conditions. By means of the uncertainty exponent, we characterise the basin boundaries between the coherent and chimera states, and between the incoherent and chimera states. This way, we show that the density of chimera states can be not only moderately sensitive but also highly sensitive to initial conditions. This chimera{\textquoteright}s dilemma is a consequence of the fractal and riddled nature of the basin boundaries.",

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author = "V. Santos and {Szezech Jr}, {J. D.} and Batista, {A. M.} and Iarosz, {K. C.} and Baptista, {M. S.} and Ren, {H. P.} and C. Grebogi and Viana, {R. L.} and Caldas, {I. L.} and Maistrenko, {Y. L.} and J. Kurths",

note = "We wish to acknowledge the support: Sao Paulo Research Foundation (FAPESP) under Grants 2011/19296-1, 2015/05186-0, 2015/07311-7, 2015/50122-0, and 2017/20920-8, Conselho Nacional de Desenvolvimento Cientıfico e Tecnologico (CNPq), and Coordena¸cao de Aperfei¸coamento de Pessoal de Nıvel Superior (CAPES).",

year = "2018",

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doi = "10.1063/1.5048595",

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publisher = "American Institute of Physics",

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T2 - Chimera’s dilemma

AU - Santos, V.

AU - Szezech Jr, J. D.

AU - Batista, A. M.

AU - Iarosz, K. C.

AU - Baptista, M. S.

AU - Ren, H. P.

AU - Grebogi, C.

AU - Viana, R. L.

AU - Caldas, I. L.

AU - Maistrenko, Y. L.

AU - Kurths, J.

N1 - We wish to acknowledge the support: Sao Paulo Research Foundation (FAPESP) under Grants 2011/19296-1, 2015/05186-0, 2015/07311-7, 2015/50122-0, and 2017/20920-8, Conselho Nacional de Desenvolvimento Cientıfico e Tecnologico (CNPq), and Coordena¸cao de Aperfei¸coamento de Pessoal de Nıvel Superior (CAPES).

PY - 2018/8

Y1 - 2018/8

N2 - We investigate the basin of attraction properties and its boundaries for chimera states in a circulant network of Hénon maps. It is known that coexisting basins of attraction lead to a hysteretic behaviour in the diagrams of the density of states as a function of a varying parameter. Chimera states, for which coherent and incoherent domains occur simultaneously, emerge as a consequence of the coexistence of basin of attractions for each state. Consequently, the distribution of chimera states can remain invariant by a parameter change, and it can also suffer subtle changes when one of the basins ceases to exist. A similar phenomenon is observed when perturbations are applied in the initial conditions. By means of the uncertainty exponent, we characterise the basin boundaries between the coherent and chimera states, and between the incoherent and chimera states. This way, we show that the density of chimera states can be not only moderately sensitive but also highly sensitive to initial conditions. This chimera’s dilemma is a consequence of the fractal and riddled nature of the basin boundaries.

AB - We investigate the basin of attraction properties and its boundaries for chimera states in a circulant network of Hénon maps. It is known that coexisting basins of attraction lead to a hysteretic behaviour in the diagrams of the density of states as a function of a varying parameter. Chimera states, for which coherent and incoherent domains occur simultaneously, emerge as a consequence of the coexistence of basin of attractions for each state. Consequently, the distribution of chimera states can remain invariant by a parameter change, and it can also suffer subtle changes when one of the basins ceases to exist. A similar phenomenon is observed when perturbations are applied in the initial conditions. By means of the uncertainty exponent, we characterise the basin boundaries between the coherent and chimera states, and between the incoherent and chimera states. This way, we show that the density of chimera states can be not only moderately sensitive but also highly sensitive to initial conditions. This chimera’s dilemma is a consequence of the fractal and riddled nature of the basin boundaries.

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M3 - Article

SN - 1054-1500

VL - 28

JO - Chaos

JF - Chaos

IS - 8

M1 - 081105

ER -

Riddling: Chimera’s dilemma

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