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Search reliability and search efficiency of combined Levy-Brownian motion: long relocations mingled with thorough local exploration

  • A combined dynamics consisting of Brownian motion and Levy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Levy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Levy flights with stable exponent alpha < 1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent a of the Levy flight component.

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Metadaten
Author:Vladimir V. Palyulin, Aleksei V. Chechkin, Rainer Klages, Ralf Metzler
DOI:https://doi.org/10.1088/1751-8113/49/39/394002
ISSN:1751-8113
ISSN:1751-8121
Parent Title (English):Journal of physics : A, Mathematical and theoretical
Publisher:IOP Publ. Ltd.
Place of publication:Bristol
Document Type:Article
Language:English
Year of first Publication:2016
Year of Completion:2016
Release Date:2020/03/22
Tag:Brownian motion; Levy flights; first arrival; first passage; random search process
Volume:49
Pagenumber:21
First Page:2189
Last Page:2193
Funder:Academy of Finland
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert