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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

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Compact Global Chaotic Attractors of Discrete Control Systems

David Cheban
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  • State University of Moldova Department of Mathematics and Informatics A. Mateevich Street 60 MD–2009 Chi³in˘au, Moldova
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Published Online: 2013-07-03 | DOI: https://doi.org/10.2478/msds-2013-0002

Abstract

The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fv(n)(xn), where v: Z+ → {1; 2; : : : ;m}. If m≥2 we give sufficient conditions (the family M := {f1; f2; : : : ; fm} of functions is contracting in the extended sense) for the existence of a compact global chaotic attractor. We study this problem in the framework of non-autonomous dynamical systems (cocycles)

Keywords: Global attractor; set-valued dynamical system; control system; chaotic attractor; collage; cocycle

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About the article

Received: 2012-10-26

Accepted: 2013-06-14

Published Online: 2013-07-03

Published in Print: 2014-01-01


Citation Information: Nonautonomous Dynamical Systems, ISSN (Online) 2353-0626, DOI: https://doi.org/10.2478/msds-2013-0002.

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© 2013 David Cheban. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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[1]
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Entropy, 2013, Volume 15, Number 8, Page 3100

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