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 journalArticlepeer-review

14 Citations (Scopus)


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 languageEnglish
Article number083115
Number of pages8
Issue number8
Early online date4 Aug 2020
Publication statusPublished - 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.




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