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 Rössler oscillators. The Rössler 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.
Skip Nav Destination
,
,
,
,
,
,
,
Article navigation
August 2020
Research Article|
August 04 2020
Basin of attraction for chimera states in a network of Rössler oscillators Available to Purchase
Special Collection:
Chaos: From Theory to Applications
Vagner dos Santos
;
Vagner dos Santos
a)
1
Program of Post-graduation in Science, State University of Ponta Grossa
, Ponta Grossa, Paraná 84030-900, Brazil
a)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
Fernando S. Borges
;
Fernando S. Borges
2
Center for Mathematics, Computation and Cognition, Federal University of ABC
, São Bernardo do Campo, São Paulo 09606-045, Brazil
Search for other works by this author on:
Kelly C. Iarosz
;
Kelly C. Iarosz
3
Institute of Physics, University of São Paulo
, São Paulo 05508-900, Brazil
4
Faculdade de Telêmaco Borba, FATEB
, Telêmaco Borba, Paraná 84266-010, Brazil
5
Graduate Program in Chemical Engineering, Federal Technological University of Paraná
, Ponta Grossa, Paraná 84016-210, Brazil
Search for other works by this author on:
Iberê L. Caldas
;
Iberê L. Caldas
3
Institute of Physics, University of São Paulo
, São Paulo 05508-900, Brazil
Search for other works by this author on:
J. D. Szezech
;
J. D. Szezech
1
Program of Post-graduation in Science, State University of Ponta Grossa
, Ponta Grossa, Paraná 84030-900, Brazil
6
Department of Mathematics and Statistics, State University of Ponta Grossa
, Ponta Grossa, Paraná 84030-900, Brazil
Search for other works by this author on:
Ricardo L. Viana
;
Ricardo L. Viana
7
Department of Physics, Federal University of Paraná
, Curitiba, Paraná 80060-000, Brazil
Search for other works by this author on:
Murilo S. Baptista
;
Murilo S. Baptista
8
Institute for Complex Systems and Mathematical Biology, University of Aberdeen
, AB24 3UE Aberdeen, Scotland, United Kingdom
Search for other works by this author on:
Antonio M. Batista
Antonio M. Batista
1
Program of Post-graduation in Science, State University of Ponta Grossa
, Ponta Grossa, Paraná 84030-900, Brazil
3
Institute of Physics, University of São Paulo
, São Paulo 05508-900, Brazil
6
Department of Mathematics and Statistics, State University of Ponta Grossa
, Ponta Grossa, Paraná 84030-900, Brazil
Search for other works by this author on:
Vagner dos Santos
1,a)
Fernando S. Borges
2
Kelly C. Iarosz
3,4,5
Iberê L. Caldas
3
J. D. Szezech
1,6
Ricardo L. Viana
7
Murilo S. Baptista
8
Antonio M. Batista
1,3,6
1
Program of Post-graduation in Science, State University of Ponta Grossa
, Ponta Grossa, Paraná 84030-900, Brazil
2
Center for Mathematics, Computation and Cognition, Federal University of ABC
, São Bernardo do Campo, São Paulo 09606-045, Brazil
3
Institute of Physics, University of São Paulo
, São Paulo 05508-900, Brazil
4
Faculdade de Telêmaco Borba, FATEB
, Telêmaco Borba, Paraná 84266-010, Brazil
5
Graduate Program in Chemical Engineering, Federal Technological University of Paraná
, Ponta Grossa, Paraná 84016-210, Brazil
6
Department of Mathematics and Statistics, State University of Ponta Grossa
, Ponta Grossa, Paraná 84030-900, Brazil
7
Department of Physics, Federal University of Paraná
, Curitiba, Paraná 80060-000, Brazil
8
Institute for Complex Systems and Mathematical Biology, University of Aberdeen
, AB24 3UE Aberdeen, Scotland, United Kingdom
a)Author to whom correspondence should be addressed: [email protected]
Note: This paper is part of the Focus Issue, Chaos: From Theory to Applications.
Chaos 30, 083115 (2020)
Article history
Received:
May 15 2020
Accepted:
July 20 2020
Citation
Vagner dos Santos, Fernando S. Borges, Kelly C. Iarosz, Iberê L. Caldas, J. D. Szezech, Ricardo L. Viana, Murilo S. Baptista, Antonio M. Batista; Basin of attraction for chimera states in a network of Rössler oscillators. Chaos 1 August 2020; 30 (8): 083115. https://doi.org/10.1063/5.0014013
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Rogue waves: Theory, methods, and applications—30 years after the Draupner wave
Zhenya Yan, Boris A. Malomed, et al.
Enhancing reservoir predictions of chaotic time series by incorporating delayed values of input and reservoir variables
Luk Fleddermann, Sebastian Herzog, et al.
Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology
Eugene Tan, Shannon Algar, et al.
Related Content
Dynamics of coupled modified Rössler oscillators: The role of nonisochronicity parameter
Chaos (May 2021)
Riddling: Chimera’s dilemma
Chaos (August 2018)
Aging in global networks with competing attractive—Repulsive interaction
Chaos (December 2020)
Synchronization transition from chaos to limit cycle oscillations when a locally coupled chaotic oscillator grid is coupled globally to another chaotic oscillator
Chaos (March 2020)
Chimera-like states induced by additional dynamic nonlocal wirings
Chaos (June 2020)