Probabilistic control of Chaos: Chaotic maps under control

Recently, we have proposed a new probabilistic method for the control of chaotic systems [1]. In this paper, we apply our method to characteristic cases of chaotic maps (one- and two-dimensional examples). As these chaotic maps are structurally stable, they cannot be controlled using conventional co...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 34; no. 2; pp. 373 - 389
Main Authors Antoniou, I., Basios, V., Bosco, F.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.1997
Subjects
Chaos
Control
Probabilistic approach
Chaos
Control
Maps
Probabilistic approach
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Summary:Recently, we have proposed a new probabilistic method for the control of chaotic systems [1]. In this paper, we apply our method to characteristic cases of chaotic maps (one- and two-dimensional examples). As these chaotic maps are structurally stable, they cannot be controlled using conventional control methods without significant change of the dynamics. Our method consists in the probabilistic coupling of the original system with a controlling system. This coupling can be understood as a feedback control of probabilistic nature. The chosen periodic orbit of the original system is a global attractor for the probability densities. The generalized spectral decomposition of the associated Frobenius-Perron operator provides a spectral condition of controllability for chaotic dynamical systems.
ISSN:0898-1221
1873-7668
DOI:10.1016/S0898-1221(97)00134-X