Bursts in average lifetime of transients for chaotic logistic map with a hole

Paar, Vladimir and Pavin, Nenad (1997) Bursts in average lifetime of transients for chaotic logistic map with a hole. Physical Review E, 55 (4). pp. 4112-4115. ISSN 1539-3755

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Abstract

Chaotic transients are studied for a logistic map at r=4, with an inserted narrow hole. We find that average lifetime τ of chaotic transients that are dependent on the hole position roughly follows the Frobenius-Perron semicircle pattern in most of the unit interval, but at the positions that correspond to the low period (1,2,3,ldots), unstable periodic orbits of the logistic map at r=4 there are bursts of τ. An asymptotic relation between the Frobenius-Perron and Kantz-Grassberger average lifetimes, at these positions, is obtained and explained in terms of missing preimages determined from a transient time map. The addition of noise leads to the destruction of bursts of average lifetime.

Item Type: Article
Keywords: classical chaos, logistic equation, nonlinearity
Date: April 1997
Subjects: NATURAL SCIENCES > Physics
Additional Information: Copyright (1997) 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: 10 Jul 2014 11:46
Last Modified: 10 Jul 2014 11:46
URI: http://digre.pmf.unizg.hr/id/eprint/1328

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