TY  - JOUR
A1  - Palyulin, Vladimir V.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias
JF  - Journal of statistical mechanics: theory and experiment
N2  - Based on the space-fractional Fokker-Planck equation with a delta-sink term, we study the efficiency of random search processes based on Levy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the preference of the searcher based on prior experience. While Levy flights turn out to be efficient search processes when the target is upstream relative to the starting point, in the downstream scenario, regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Levy flights, due to which Levy flights typically overshoot a point or small interval. Studying the solution of the fractional Fokker-Planck equation, we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favours Levy flights over the regular Brownian search. Contrary to the common belief that Levy flights with a Levy index alpha = 1 (i.e. Cauchy flights) are optimal for sparse targets, we find that the optimal value for alpha may range in the entire interval (1, 2) and explicitly include Brownian motion as the most efficient search strategy overall.
KW  - driven diffusive systems (theory)
KW  - fluctuations (theory)
KW  - stochastic processes (theory)
KW  - diffusion
Y1  - 2014
U6  - https://doi.org/10.1088/1742-5468/2014/11/P11031
SN  - 1742-5468
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Palyulin, Vladimir V.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Levy flights do not always optimize random blind search for sparse targets
JF  - Proceedings of the National Academy of Sciences of the United States of America
N2  - It is generally believed that random search processes based on scale-free, Levy stable jump length distributions (Levy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Levy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Levy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Levy flights with a critical exponent alpha = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal a may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.
KW  - search optimization
KW  - stochastic processes
KW  - Levy foraging hypothesis
Y1  - 2014
U6  - https://doi.org/10.1073/pnas.1320424111
SN  - 0027-8424
VL  - 111
IS  - 8
SP  - 2931
EP  - 2936
PB  - National Acad. of Sciences
CY  - Washington
ER  -