Almost periodicity in chaos

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dc.contributor.author Akhmet, M.
dc.contributor.author Fen, M.O.
dc.date.accessioned 2019-07-25T14:27:16Z
dc.date.available 2019-07-25T14:27:16Z
dc.date.issued 2018
dc.identifier.issn 21646376
dc.identifier.uri https://doi.org/10.5890/DNC.2018.03.002
dc.identifier.uri http://hdl.handle.net/20.500.12485/451
dc.description.abstract Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one obtained through period-doubling cascade [3]. Countable number of periodic orbits exist in any neighborhood of a structurally stable Poincaré homoclinic orbit, which can be considered as a criterion for the presence of complex dynamics [4-6]. It was certified by Shilnikov [7] and Seifert [8] that it is possible to replace periodic solutions by Poisson stable or almost periodic motions in a chaotic attractor. Despite the fact that the idea of replacing periodic solutions by other types of regular motions is attractive, very few results have been obtained on the subject. The present study contributes to the chaos theory in that direction. In this paper, we take into account chaos both through a cascade of almost periodic solutions and in the sense of Li-Yorke such that the original Li-Yorke definition is modified by replacing infinitely many periodic motions with almost periodic ones, which are separated from the motions of the scrambled set. The theoretical results are valid for systems with arbitrary high dimensions. Formation of the chaos is exemplified by means of unidirectionally coupled Duffing oscillators. The controllability of the extended chaos is demonstrated numericallyby means of the Ott-Grebogi-Yorke [9] control technique. In particular, the stabilization of tori is illustrated. © 2018 L&H Scientific Publishing, LLC. All rights reserved. en_US
dc.language.iso en en_US
dc.publisher L and H Scientific Publishing, LLC en_US
dc.subject Cellular neural networks en_US
dc.subject Chaos theory en_US
dc.subject Chaos en_US
dc.title Almost periodicity in chaos en_US
dc.type Article en_US
dc.relation.journal Discontinuity, Nonlinearity, and Complexity en_US
dc.contributor.authorID http://orcid.org/0000-0002-7787-7236 en_US
dc.identifier.issue 1 en_US
dc.identifier.startpage 15 en_US
dc.identifier.endpage 29 en_US
dc.identifier.volume 7 en_US

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