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 languageEnglish
Article number081105
Number of pages6
JournalChaos
Volume28
Issue number8
Early online date23 Aug 2018
DOIs
Publication statusPublished - Aug 2018

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Dilemma
Basin of Attraction
Fractals
Density of States
Initial conditions
attraction
Coexistence
Fractal
Diagram
Exponent
Perturbation
Uncertainty
Invariant
fractals
diagrams
exponents
perturbation

Keywords

  • nlin.CD

Cite this

Santos, V., Szezech Jr, J. D., Batista, A. M., Iarosz, K. C., Baptista, M. S., Ren, H. P., ... Kurths, J. (2018). Riddling: Chimera’s dilemma . Chaos, 28(8), [081105]. https://doi.org/10.1063/1.5048595

Riddling : Chimera’s dilemma . / Santos, V.; Szezech Jr, J. D.; Batista, A. M.; Iarosz, K. C.; Baptista, M. S.; Ren, H. P.; Grebogi, C.; Viana, R. L.; Caldas, I. L.; Maistrenko, Y. L.; Kurths, J.

In: Chaos, Vol. 28, No. 8, 081105, 08.2018.

Research output: Contribution to journalArticle

Santos, V, Szezech Jr, JD, Batista, AM, Iarosz, KC, Baptista, MS, Ren, HP, Grebogi, C, Viana, RL, Caldas, IL, Maistrenko, YL & Kurths, J 2018, 'Riddling: Chimera’s dilemma ', Chaos, vol. 28, no. 8, 081105. https://doi.org/10.1063/1.5048595
Santos V, Szezech Jr JD, Batista AM, Iarosz KC, Baptista MS, Ren HP et al. Riddling: Chimera’s dilemma . Chaos. 2018 Aug;28(8). 081105. https://doi.org/10.1063/1.5048595
Santos, V. ; Szezech Jr, J. D. ; Batista, A. M. ; Iarosz, K. C. ; Baptista, M. S. ; Ren, H. P. ; Grebogi, C. ; Viana, R. L. ; Caldas, I. L. ; Maistrenko, Y. L. ; Kurths, J. / Riddling : Chimera’s dilemma . In: Chaos. 2018 ; Vol. 28, No. 8.
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AU - Maistrenko, Y. L.

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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.

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