Identification of single- and double-well coherence–incoherence patterns by the 
binary distance matrix

dos Santos, Vagner; Sales, Matheus Rolim; Muni, Sishu Shankar; Szezech, José Danilo; Batista, Antonio Marcos; Yanchuk, Serhiy; Kurths, Jürgen

doi:10.1016/j.cnsns.2023.107390

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Identification of single- and double-well coherence–incoherence patterns by the binary distance matrix

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dos Santos, Vagner
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Sales, Matheus Rolim
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Muni, Sishu Shankar
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Szezech, José Danilo
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Batista, Antonio Marcos
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Yanchuk, Serhiy
Potsdam Institute for Climate Impact Research;

/persons/resource/Juergen.Kurths

Kurths, Jürgen
Potsdam Institute for Climate Impact Research;

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Citation

dos Santos, V., Sales, M. R., Muni, S. S., Szezech, J. D., Batista, A. M., Yanchuk, S., Kurths, J. (2023): Identification of single- and double-well coherence–incoherence patterns by the binary distance matrix. - Communications in Nonlinear Science and Numerical Simulation, 125, 107390.
https://doi.org/10.1016/j.cnsns.2023.107390

Cite as: https://publications.pik-potsdam.de/pubman/item/item_28948

Abstract

The study of chimera states or, more generally, coherence–incoherence patterns has led to the development of several tools for their identification and characterization. In this work, we extend the eigenvalue decomposition method to distinguish between single-well (SW) and double-well (DW) patterns. By applying our method, we are able to identify the following four types of dynamical patterns in a ring of nonlocally coupled Chua circuits and nonlocally coupled cubic maps: SW cluster, SW coherence–incoherence pattern, DW cluster, and DW coherence–incoherence. In a ring-star network of Chua circuits, we investigate the influence of adding a central node on the spatio-temporal patterns. Our results show that increasing the coupling with the central node favors the occurrence of SW coherence–incoherence states. We observe that the boundaries of the attraction basins resemble fractal and riddled structures.