Compact Global Chaotic Attractors of Discrete Control Systems

• Autorzy: David Cheban
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Nonautonomous Dynamical Systems
• Rocznik: 2014
• Tom: 1

Daty

otrzymano

2012-10-26

zaakceptowano

2013-06-10

online

2013-07-03

Twórcy

autor

David Cheban

• State University of Moldova
  Department of Mathematics and Informatics
  A. Mateevich Street 60
  MD–2009 Chi³in˘au, Moldova,

Bibliografia

• [1] V. M. Alekseev, Symbolic Dynamics, The 11th Mathematical School. Kiev, Naukova Dumka, 1986.
• [2] M. F. Barnsley, Fractals everywhere, New York, Academic Press, 1988.
• [3] N. A. Bobylev, S. V. Emel’yanov, S. K. Korovin, Attractors of Discrete Controlled Systems in Metric Spaces. ComputationalMathematics and Modeling, 11 (2000), 321–326; Translated from Prikladnaya Mathematika i Informatika,3, (1999), 5–10.
• [4] V. A. Bondarenko, V. L. Dolnikov, Fractal Image Compression by The Barnsley-Sloan Method, Automation andRemote Control, 55, (1994), 623–629; Translated from Avtomatika i Telemekhanika, 5, (1994), 12–20.
• [5] H. Brezis, Operateurs Maximaux Monotones et Semigroupes de Contractions dans les Espaces de Hilbert,Math.Studies, 5, North Holland, 1973.
• [6] D. N. Cheban, Global Attractors of Nonautonomous Dissipstive Dynamical Systems. Interdisciplinary MathematicalSciences, 1, River Edge, New Jersey, World Scientific, 2004.
• [7] D. N. Cheban, Compact Global Attractors of Control Systems. Journal of Dynamical and Control Systems, 16(2010), 23–44.[WoS][Crossref]
• [8] D. N. Cheban, Global Attractors of Set-Valued Dynamical and Control Systems. Nova Science Publishers Inc, NewYork, 2010.
• [9] D. N. Cheban, C. Mammana, Global Compact Attractors of Discrete Inclusions. Nonlinear Analyses: TMA, 65,(2006), 1669–1687.
• [10] D. N. Cheban, B. Schmalfuss, Invariant Manifolds, Global Attractors, Almost Automrphic and Almost PeriodicSolutions of Non-Autonomous Differential Equations. J. Math. Anal. Appl., 340, (2008), 374–393.[WoS]
• [11] L. Gurvits, Stability of Discrete Linear Inclusion. Linear Algebra Appl., 231 (1995), 47–85.
• [12] B. M. Levitan, V. V. Zhikov, Almost Periodic Functions and Differential Equations. Moscow State University Press,1978. (in Russian) [English translation in Cambridge Univ. Press, Cambridge, 1982.]
• [13] J. L. Lions, Quelques Methodes de Résolution des Problèmes aux Limites non Linéaires. Dunod, Paris, 1969.
• [14] C. Robinson, Dynamical Systems: Stabilty, Symbolic Dynamics and Chaos (Studies in Advanced Mathematics).Boca Raton Florida, CRC Press, 1995.
• [15] G. R. Sell, Topological Dynamics and Ordinary Differential Equations. Van Nostrand-Reinhold, London, 1971.
• [16] B. A. Shcherbakov, Topological Dynamics and Poisson’s Stability of Solutions of Differential Equations. Kishinev,Shtiintsa, 1972 (in Russian).
• [17] K. S. Sibirskii, A. S. Shube, Semidynamical Systems. Stiintsa, Kishinev 1987 (in Russian).

Identyfikatory

DOI

10.2478/msds-2013-0002