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Improvements in the statistical approach to random Lévy flight searches

Author

Listed:
  • da Luz, M.G.E
  • Buldyrev, Sergey V
  • Havlin, Shlomo
  • Raposo, E.P
  • Stanley, H.Eugene
  • Viswanathan, G.M

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.

Suggested Citation

  • da Luz, M.G.E & Buldyrev, Sergey V & Havlin, Shlomo & Raposo, E.P & Stanley, H.Eugene & Viswanathan, G.M, 2001. "Improvements in the statistical approach to random Lévy flight searches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 89-92.
    • Handle: RePEc:eee:phsmap:v:295:y:2001:i:1:p:89-92
    DOI: 10.1016/S0378-4371(01)00058-9
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    Citations

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    Cited by:

    1. Ferreira, A.S. & Raposo, E.P. & Viswanathan, G.M. & da Luz, M.G.E., 2012. "The influence of the environment on Lévy random search efficiency: Fractality and memory effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3234-3246.
    2. E P Raposo & F Bartumeus & M G E da Luz & P J Ribeiro-Neto & T A Souza & G M Viswanathan, 2011. "How Landscape Heterogeneity Frames Optimal Diffusivity in Searching Processes," PLOS Computational Biology, Public Library of Science, vol. 7(11), pages 1-8, November.
    3. Sepideh Bazazi & Frederic Bartumeus & Joseph J Hale & Iain D Couzin, 2012. "Intermittent Motion in Desert Locusts: Behavioural Complexity in Simple Environments," PLOS Computational Biology, Public Library of Science, vol. 8(5), pages 1-10, May.
    4. Marina E Wosniack & Marcos C Santos & Ernesto P Raposo & Gandhi M Viswanathan & Marcos G E da Luz, 2017. "The evolutionary origins of Lévy walk foraging," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-31, October.

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