Asymmetric Levy flights are more efficient in random search
- We study the first-arrival (first-hitting) dynamics and efficiency of a one-dimensional random search model performing asymmetric Levy flights by leveraging the Fokker-Planck equation with a delta-sink and an asymmetric space-fractional derivative operator with stable index alpha and asymmetry (skewness) parameter beta. We find exact analytical results for the probability density of first-arrival times and the search efficiency, and we analyse their behaviour within the limits of short and long times. We find that when the starting point of the searcher is to the right of the target, random search by Brownian motion is more efficient than Levy flights with beta <= 0 (with a rightward bias) for short initial distances, while for beta>0 (with a leftward bias) Levy flights with alpha -> 1 are more efficient. When increasing the initial distance of the searcher to the target, Levy flight search (except for alpha=1 with beta=0) is more efficient than the Brownian search. Moreover, the asymmetry in jumps leads to essentiallyWe study the first-arrival (first-hitting) dynamics and efficiency of a one-dimensional random search model performing asymmetric Levy flights by leveraging the Fokker-Planck equation with a delta-sink and an asymmetric space-fractional derivative operator with stable index alpha and asymmetry (skewness) parameter beta. We find exact analytical results for the probability density of first-arrival times and the search efficiency, and we analyse their behaviour within the limits of short and long times. We find that when the starting point of the searcher is to the right of the target, random search by Brownian motion is more efficient than Levy flights with beta <= 0 (with a rightward bias) for short initial distances, while for beta>0 (with a leftward bias) Levy flights with alpha -> 1 are more efficient. When increasing the initial distance of the searcher to the target, Levy flight search (except for alpha=1 with beta=0) is more efficient than the Brownian search. Moreover, the asymmetry in jumps leads to essentially higher efficiency of the Levy search compared to symmetric Levy flights at both short and long distances, and the effect is more pronounced for stable indices alpha close to unity.…
Author details: | Amin PadashORCiD, Trifce SandevORCiDGND, Holger KantzORCiDGND, Ralf MetzlerORCiDGND, Aleksei ChechkinORCiDGND |
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DOI: | https://doi.org/10.3390/fractalfract6050260 |
ISSN: | 2504-3110 |
Title of parent work (English): | Fractal and fractional |
Publisher: | MDPI |
Place of publishing: | Basel |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/05/08 |
Publication year: | 2022 |
Release date: | 2024/05/27 |
Tag: | asymmetric Levy flights; first-arrival density; search efficiency |
Volume: | 6 |
Issue: | 5 |
Article number: | 260 |
Number of pages: | 23 |
Funding institution: | Alexander von Humboldt Foundation; German Science Foundation (DFG) [ME; 1535/12-1]; Foundation for Polish Science (Fundacja na rzecz Nauki; Polskiej, FNR) within an Alexander von Humboldt Honorary Polish Research; Scholarship; Polish National Agency for Academic Exchange (NAWA);; bilateral Macedonian-Chinese research project - inter-governmental; Macedonian-Chinese agreement [20-6333] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 52 Astronomie / 520 Astronomie und zugeordnete Wissenschaften |
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
Peer review: | Referiert |
Publishing method: | Open Access / Gold Open-Access |
DOAJ gelistet | |
License (German): | CC-BY - Namensnennung 4.0 International |