Improvements in the statistical approach to random Lévy flight searches

M. G.E. Da Luz; Sergey V. Buldyrev; Shlomo Havlin; E. P. Raposo; H. Eugene Stanley; G. M. Viswanathan

doi:10.1016/s0378-4371(01)00058-9

Improvements in the statistical approach to random Lévy flight searches

M. G.E. Da Luz, Sergey V. Buldyrev, Shlomo Havlin, E. P. Raposo, H. Eugene Stanley, G. M. Viswanathan

Department of Physics

Research output: Contribution to journal › Conference article › peer-review

45 Scopus citations

Abstract

Recently it has been shown that the most efficient strategy for searching randomly located objects, when the sites are randomly distributed and can be revisited any number of times, leads to a power law distribution P(ℓ) = ℓ^-μ of the flights ℓ, with μ = 2. We show analytically that the incorporation of energy considerations limits the possible range for the Lévy exponent μ, however, μ = 2 still emerges as the optimal foraging condition. Furthermore, we show that the probability distribution of flight lengths for the short and intermediate flight length regimes depends on the details of the system.

Original language	English
Pages (from-to)	89-92
Number of pages	4
Journal	Physica A: Statistical Mechanics and its Applications
Volume	295
Issue number	1-2
DOIs	https://doi.org/10.1016/s0378-4371(01)00058-9
State	Published - 1 Jun 2001
Event	Proceedings of the IUPAP International Conference on New Trends in the Fractal Aspects of Complex Systems - Maceio, Brazil Duration: 16 Oct 2000 → 20 Oct 2000

Bibliographical note

Funding Information:
This work was supported by the Brazilian agencies CNPq, FAPEAL, FNS, NIH, FACEPE and PRPPG (UFPR).

Keywords

Energy constraint
Foraging
Lévy distribution
Short flight regime

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10.1016/s0378-4371(01)00058-9

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abstract = "Recently it has been shown that the most efficient strategy for searching randomly located objects, when the sites are randomly distributed and can be revisited any number of times, leads to a power law distribution P(ℓ) = ℓ-μ of the flights ℓ, with μ = 2. We show analytically that the incorporation of energy considerations limits the possible range for the L{\'e}vy exponent μ, however, μ = 2 still emerges as the optimal foraging condition. Furthermore, we show that the probability distribution of flight lengths for the short and intermediate flight length regimes depends on the details of the system.",

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AU - Buldyrev, Sergey V.

AU - Havlin, Shlomo

AU - Raposo, E. P.

AU - Stanley, H. Eugene

AU - Viswanathan, G. M.

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N2 - Recently it has been shown that the most efficient strategy for searching randomly located objects, when the sites are randomly distributed and can be revisited any number of times, leads to a power law distribution P(ℓ) = ℓ-μ of the flights ℓ, with μ = 2. We show analytically that the incorporation of energy considerations limits the possible range for the Lévy exponent μ, however, μ = 2 still emerges as the optimal foraging condition. Furthermore, we show that the probability distribution of flight lengths for the short and intermediate flight length regimes depends on the details of the system.

AB - Recently it has been shown that the most efficient strategy for searching randomly located objects, when the sites are randomly distributed and can be revisited any number of times, leads to a power law distribution P(ℓ) = ℓ-μ of the flights ℓ, with μ = 2. We show analytically that the incorporation of energy considerations limits the possible range for the Lévy exponent μ, however, μ = 2 still emerges as the optimal foraging condition. Furthermore, we show that the probability distribution of flight lengths for the short and intermediate flight length regimes depends on the details of the system.

KW - Energy constraint

KW - Foraging

KW - Lévy distribution

KW - Short flight regime

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Improvements in the statistical approach to random Lévy flight searches

Abstract

Bibliographical note

Keywords

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