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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
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. 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.
    9. Willis, Jay, 2011. "Modelling swimming aquatic animals in hydrodynamic models," Ecological Modelling, Elsevier, vol. 222(23), pages 3869-3887.

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