Dec 3 – 4, 2020
Europe/Warsaw timezone

Search efficiency of (discrete) fractional Brownian motion in a random distribution of targets

Dec 3, 2020, 6:09 PM


Seyed Mohsen Jebreiil Khadem (Technische Universität Berlin)


Efficiency of search for randomly distributed targets is a prominent problem in many branches
of the sciences. For the stochastic process of Lévy walks, a specific range of optimal efficiencies
was suggested under variation of search intrinsic and extrinsic environmental parameters. We study fractional Brownian motion as a search process, which under parameter variation
generates all three basic types of diffusion, from sub- to normal to superdiffusion. In contrast to Lévy
walks, fractional Brownian motion defines a Gaussian stochastic process with power law memory
yielding anti-persistent, respectively persistent motion. Computer simulations of this search process
in a uniformly random distribution of targets show that maximising search efficiencies sensitively
depends on the definition of efficiency, the variation of both intrinsic and extrinsic parameters, the
perception of targets, the type of targets, whether to detect only one or many of them, and the
choice of boundary conditions. We find that different search scenarios favour different modes of
motion for optimising search success, defying a universality across all search situations. Some of our
results are explained by a simple analytical model. Having demonstrated that search by fractional
Brownian motion is a truly complex process, we propose an over-arching conceptual framework
based on classifying different search scenarios. This approach incorporates search optimisation by
Lévy walks as a special case.

Primary authors

Seyed Mohsen Jebreiil Khadem (Technische Universität Berlin) Prof. Sabine H.L. Klapp (Technische Universität Berlin) Rainer Klages (Queen Mary University of London)

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