Basins of Attraction: From unidimensional maps to complex networks
Study of collective phenomena in physical and biological systems
| Full text | |
| Author(s): |
dos Santos, Vagner
[1]
;
Borges, Fernando S.
[2]
;
Iarosz, Kelly C.
[3, 4, 5]
;
Caldas, Ibere L.
[3]
;
Szezech, J. D.
[1, 6]
;
Viana, Ricardo L.
[7]
;
Baptista, Murilo S.
[8]
;
Batista, Antonio M.
[3, 1, 6]
Total Authors: 8
|
| Affiliation: | [1] Univ Estadual Ponta Grossa, Program Postgrad Sci, BR-84030900 Ponta Grossa, Parana - Brazil
[2] Fed Univ ABC, Ctr Math Computat & Cognit, BR-09606045 Sao Bernardo Do Campo, SP - Brazil
[3] Univ Sao Paulo, Inst Phys, BR-05508900 Sao Paulo - Brazil
[4] FATEB, Fac Telemaco Borba, BR-84266010 Telemaco Borba, Parana - Brazil
[5] Fed Technol Univ Parana, Grad Program Chem Engn, BR-84016210 Ponta Grossa, Parana - Brazil
[6] Univ Estadual Ponta Grossa, Dept Math & Stat, BR-84030900 Ponta Crossa, Parana - Brazil
[7] Univ Fed Parana, Dept Phys, BR-80060000 Curitiba, Parana - Brazil
[8] Univ Aberdeen, Inst Complex Syst & Math Biol, Aberdeen AB24 3UE - Scotland
Total Affiliations: 8
|
| Document type: | Journal article |
| Source: | Chaos; v. 30, n. 8 AUG 2020. |
| Web of Science Citations: | 0 |
| 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. (AU) | |
| FAPESP's process: | 18/03211-6 - Non linear dynamics |
| Grantee: | Iberê Luiz Caldas |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 15/07311-7 - Dynamic behaviour of neural networks |
| Grantee: | Kelly Cristiane Iarosz |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 17/18977-1 - Analysis of Electrical Synapses Contribution in Neuronal Synchronization |
| Grantee: | Fernando da Silva Borges |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |