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

Scientific paper - Original scientific paper

• Author: Vladimir Paar
• Author: Nenad Pavin
• Author's institution: University of Zagreb; Faculty of Science; (Department of Physics)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract (english)

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.

• Keywords (english): classical chaos; logistic equation; nonlinearity
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Physical Review E
• Numbering: vol. 55, no. 4, pp. 4112-4115
• p-ISSN: 1539-3755
• DOI: https://doi.org/10.1103/PhysRevE.55.4112
• URN:NBN: urn:nbn:hr:217:033675
• Publication: 1997
• Document URL: http://link.aps.org/doi/10.1103/PhysRevE.55.4112
• Type of resource: Text
• Access conditions: Open access
• Public note: Copyright (1997) by the American Physical Society.
• Created on: 2019-10-04 15:54:46