Compact Global Chaotic Attractors of Discrete Control Systems

David Cheban

Nonautonomous Dynamical Systems (2014)

  • Volume: 1, page 10-25, electronic only
  • ISSN: 2353-0626

Abstract

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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 = fν(n)(xn), where ν : 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).

How to cite

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David Cheban. "Compact Global Chaotic Attractors of Discrete Control Systems." Nonautonomous Dynamical Systems 1 (2014): 10-25, electronic only. <http://eudml.org/doc/266954>.

@article{DavidCheban2014,
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 = fν(n)(xn), where ν : 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).},
author = {David Cheban},
journal = {Nonautonomous Dynamical Systems},
keywords = {Global attractor; set-valued dynamical system; control system; chaotic attractor; collage; cocycle; global attractor},
language = {eng},
pages = {10-25, electronic only},
title = {Compact Global Chaotic Attractors of Discrete Control Systems},
url = {http://eudml.org/doc/266954},
volume = {1},
year = {2014},
}

TY - JOUR
AU - David Cheban
TI - Compact Global Chaotic Attractors of Discrete Control Systems
JO - Nonautonomous Dynamical Systems
PY - 2014
VL - 1
SP - 10
EP - 25, electronic only
AB - 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 = fν(n)(xn), where ν : 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).
LA - eng
KW - Global attractor; set-valued dynamical system; control system; chaotic attractor; collage; cocycle; global attractor
UR - http://eudml.org/doc/266954
ER -

References

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  13. [13] J. L. Lions, Quelques Methodes de Résolution des Problèmes aux Limites non Linéaires. Dunod, Paris, 1969. 
  14. [14] C. Robinson, Dynamical Systems: Stabilty, Symbolic Dynamics and Chaos (Studies in Advanced Mathematics). Boca Raton Florida, CRC Press, 1995. 
  15. [15] G. R. Sell, Topological Dynamics and Ordinary Differential Equations. Van Nostrand-Reinhold, London, 1971. Zbl0212.29202
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