Effect of the search space dimensionality for finding close and faraway targets in random searches

J. R. Colaço, H. A. Araújo, M. G. E. da Luz, G. M. Viswanathan, F. Bartumeus, and E. P. Raposo
Phys. Rev. E 106, 034124 – Published 15 September 2022

Abstract

We investigate the dependence on the search space dimension of statistical properties of random searches with Lévy α-stable and power-law distributions of step lengths. We find that the probabilities to return to the last target found (P0) and to encounter faraway targets (PL), as well as the associated Shannon entropy S, behave as a function of α quite differently in one (1D) and two (2D) dimensions, a somewhat surprising result not reported until now. While in 1D one always has P0PL, an interesting crossover takes place in 2D that separates the search regimes with P0>PL for higher α and P0<PL for lower α, depending on the initial distance to the last target found. We also obtain in 2D a maximum in the entropy S for α(0,2], not observed in 1D apart from the trivial α0 ballistic limit. Improving the understanding of the role of dimensionality in random searches is relevant in diverse contexts, as in the problem of encounter rates in biology and ecology.

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  • Received 10 June 2022
  • Accepted 1 September 2022

DOI:https://doi.org/10.1103/PhysRevE.106.034124

©2022 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

J. R. Colaço1, H. A. Araújo1,2, M. G. E. da Luz3, G. M. Viswanathan4, F. Bartumeus5,6,7, and E. P. Raposo1

  • 1Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife-PE, 50670-901, Brazil
  • 2Departamento de Matemática, Universidade Federal de Pernambuco, Recife-PE, 50670-901, Brazil
  • 3Departamento de Física, Universidade Federal do Paraná, Curitiba-PR, 81531-980, Brazil
  • 4Department of Physics and National Institute of Science and Technology of Complex Systems, Federal University of Rio Grande do Norte, Natal-RN, 59078-970, Brazil
  • 5Centre d'Estudis Avançats de Blanes-CEAB-CSIC, Girona, 17300, Spain
  • 6CREAF, Universitat Autònoma de Barcelona, Cerdanyola del Vallés, 08193, Spain
  • 7Institució Catalana de Recerca i Estudis Avançats-ICREA, Barcelona, 08010, Spain

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Issue

Vol. 106, Iss. 3 — September 2022

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