https://doi.org/10.1140/epjs/s11734-025-02059-z
Regular Article
Pattern characterization in non-locally coupled chaotic systems
1
Centro de Estudos do Mar, Universidade Federal do Paraná, 83255-976, Pontal do Paraná, Paraná, Brazil
2
Departamento de Física, Universidade Federal do Paraná, 81531-980, Curitiba, Paraná, Brazil
3
Centro Interdisciplinar de Ciência, Tecnologia e Inovação, Núcleo de Modelagem e Computação Científica, Universidade Federal do Paraná, Curitiba, Paraná, Brazil
a
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Received:
25
May
2025
Accepted:
3
November
2025
Published online:
9
November
2025
Abstract
We consider a model for a non-local coupling of chaotic systems, in which the interaction among them is mediated by the local concentration of a substance which diffuses along the spatial medium in which the systems are embedded. We assume that the diffusion time is vanishingly small, such that the concentration of the chemical reaches immediately its equilibrium limit. The Green function for the diffusion problem, with absorbing boundary conditions, is obtained for three geometries: bounded linear, rectangular, and circular domains. The resulting system of coupled differential equations was numerically integrated in the case that the chaotic systems are given by Rössler equations. The snapshots, or spatial patterns at fixed time, were analyzed using diagnostics of spatial coherence, such as a local order parameter based on a geometrical phase defined for each system. We analyzed the formation of chimera states, or inhomogeneous spatial patterns presenting both coherent and incoherent regions, for the three geometries considered and studied the dependence of results with the coupling parameters.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
