Many-hole interactions and the average lifetimes of chaotic transients that precede controlled periodic motion

Buljan, Hrvoje and Paar, Vladimir (2001) Many-hole interactions and the average lifetimes of chaotic transients that precede controlled periodic motion. Physical Review E, 63 (6). pp. 66205-13. ISSN 1539-3755

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Abstract

We consider n small regions (referred to as the holes) on a chaotic attractor and study the average lifetime it takes for a randomly initiated trajectory to land in their union. The holes are thought of as n possible escape routes for the trajectory. The escape route through one of the holes may be considerably reduced by other holes, depending on their positions. This effect, referred to as shadowing, can significantly prolong the average lifetime. The main result of this paper is the construction and analysis (numerical and theoretical) of the many-hole interactions. They are interpreted as the amount of shadowing between the holes. The “effective range” of these interactions is associated with the largest Lyapunov exponent. The shadowing effect is shown to be very large when the holes are located on n points of an unstable periodic orbit. Considerable attention is paid to this case since it is of interest to the field of controlling chaos.

Item Type: Article
Keywords: chaotic transients, holes on chaotic attractor, controlled periodic motion
Date: May 2001
Subjects: NATURAL SCIENCES > Physics
Additional Information: Copyright (2001) by the American Physical Society.
Divisions: Faculty of Science > Department of Physics
Project code: 119211
Publisher: American Physical Society
Depositing User: Gordana Stubičan Ladešić
Date Deposited: 23 May 2014 08:19
Last Modified: 23 May 2014 08:19
URI: http://digre.pmf.unizg.hr/id/eprint/1634

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