Chimeras confined by fractal boundaries in the complex plane

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• dc.contributor.author Andrzejak, Ralph Gregor
• dc.date.accessioned 2021-05-06T09:15:42Z
• dc.date.available 2021-05-06T09:15:42Z
• dc.date.issued 2021
• dc.description.abstract Complex-valued quadratic maps either converge to fixed points, enter into periodic cycles, show aperiodic behavior, or diverge to infinity. Which of these scenarios takes place depends on the map’s complex-valued parameter c and the initial conditions. The Mandelbrot set is defined by the set of c values for which the map remains bounded when initiated at the origin of the complex plane. In this study, we analyze the dynamics of a coupled network of two pairs of two quadratic maps in dependence on the parameter c. Across the four maps, c is kept the same whereby the maps are identical. In analogy to the behavior of individual maps, the network iterates either diverge to infinity or remain bounded. The bounded solutions settle into different stable states, including full synchronization and desynchronization of all maps. Furthermore, symmetric partially synchronized states of within-pair synchronization and across-pair synchronization as well as a symmetry broken chimera state are found. The boundaries between bounded and divergent solutions in the domain of c are fractals showing a rich variety of intriguingly esthetic patterns. Moreover, the set of bounded solutions is divided into countless subsets throughout all length scales in the complex plane. Each individual subset contains only one state of synchronization and is enclosed within fractal boundaries by c values leading to divergence.
• dc.format.mimetype application/pdf
• dc.identifier.citation Andrzejak RG. Chimeras confined by fractal boundaries in the complex plane. Chaos. 2021;31(5):053104. DOI: 10.1063/5.0049631
• dc.identifier.doi https://dx.doi.org/10.1063/5.0049631
• dc.identifier.issn 1054-1500
• dc.identifier.uri http://hdl.handle.net/10230/47339
• dc.language.iso eng
• dc.publisher American Institute of Physics (AIP)
• dc.relation.ispartof Chaos. 2021;31(5):053104
• dc.relation.isreferencedby https://doi.org/10.34810/data49
• dc.rights © American Institute of Physics. The following article appeared in Andrzejak RG, Chaos. 31(5), 2021 and may be found at https://doi.org/10.1063/5.0049631
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.title Chimeras confined by fractal boundaries in the complex plane
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion