IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v282y2000i1p1-12.html
   My bibliography  Save this article

Lévy flights in random searches

Author

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

Abstract

We review the general search problem of how to find randomly located objects that can only be detected in the limited vicinity of a forager, and discuss its quantitative description using the theory of random walks. We illustrate Lévy flight foraging by comparison to Brownian random walks and discuss experimental observations of Lévy flights in biological foraging. We review recent findings suggesting that an inverse square probability density distribution P(ℓ)∼ℓ−2 of step lengths ℓ can lead to optimal searches. Finally, we survey the explanations put forth to account for these unexpected findings.

Suggested Citation

  • Viswanathan, G.M & Afanasyev, V & Buldyrev, Sergey V & Havlin, Shlomo & da Luz, M.G.E & Raposo, E.P & Stanley, H.Eugene, 2000. "Lévy flights in random searches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 1-12.
    • Handle: RePEc:eee:phsmap:v:282:y:2000:i:1:p:1-12
    DOI: 10.1016/S0378-4371(00)00071-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437100000716
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(00)00071-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Qianqian Liu & Qun Wang, 2017. "A comparative study on uncooperative search models in survivor search and rescue," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 89(2), pages 843-857, November.
    2. 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.
    3. Liu, Yancai & Cai, Rui & Duan, Jinqiao, 2019. "Lévy noise induced escape in the Morris–Lecar model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C), pages 1-1.
    4. Zhenpeng Li & Zhihua Yan & Xijin Tang, 2024. "Evolutionary Model of Signed Edges in Online Networks Based on Infinite One-Dimensional Uniform Lattice," Mathematics, MDPI, vol. 12(7), pages 1-9, March.
    5. Jonathan U Harrison & Ruth E Baker, 2018. "The impact of temporal sampling resolution on parameter inference for biological transport models," PLOS Computational Biology, Public Library of Science, vol. 14(6), pages 1-30, June.
    6. O’Keeffe, Kevin & Santi, Paolo & Wang, Brandon & Ratti, Carlo, 2021. "Urban sensing as a random search process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    7. LaScala-Gruenewald, Diana E. & Mehta, Rohan S. & Liu, Yu & Denny, Mark W., 2019. "Sensory perception plays a larger role in foraging efficiency than heavy-tailed movement strategies," Ecological Modelling, Elsevier, vol. 404(C), pages 69-82.
    8. Qi, Jie & Rong, Zhihai, 2013. "The emergence of scaling laws search dynamics in a particle swarm optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1522-1531.
    9. Danish A Ahmed & Ali R Ansari & Mudassar Imran & Kamal Dingle & Michael B Bonsall, 2021. "Mechanistic modelling of COVID-19 and the impact of lockdowns on a short-time scale," PLOS ONE, Public Library of Science, vol. 16(10), pages 1-20, October.
    10. Wang, Zhenhai & Wang, Xudong, 2024. "Landscapes of random diffusivity processes in harmonic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    11. Willis, Jay, 2011. "Modelling swimming aquatic animals in hydrodynamic models," Ecological Modelling, Elsevier, vol. 222(23), pages 3869-3887.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:282:y:2000:i:1:p:1-12. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.