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September  2006, 6(5): 1157-1174. doi: 10.3934/dcdsb.2006.6.1157

Parametric perturbations and non-feedback controlling chaotic motion

Alexander Loskutov 1,

1. 

Physics Faculty, Moscow State University, 119992 Moscow, Russian Federation

Received  November 2005 Revised  January 2006 Published  June 2006

In this paper we generalize analytic studies the problems related to suppression of chaos and non--feedback controlling chaotic motion. We develop an analytic method of the investigation of qualitative changes in chaotic dynamical systems under certain external periodic perturbations. It is proven that for polymodal maps one can stabilize chosen in advance periodic orbits. As an example, the quadratic family of maps is considered.
    Also we demonstrate that for a piecewise linear family of maps and for a two-dimensional map having a hyperbolic attractor there are feedback-free perturbations which lead to the suppression of chaos and stabilization of certain periodic orbits.
Keywords: Chaos, suppression of chaos, periodic orbits., perturbed maps.
Mathematics Subject Classification: Primary: 58F13, 58F03; Secondary: 53F12, 58F3.
Citation: Alexander Loskutov. Parametric perturbations and non-feedback controlling chaotic motion. Discrete & Continuous Dynamical Systems - B, 2006, 6 (5) : 1157-1174. doi: 10.3934/dcdsb.2006.6.1157
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