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Pages 492-497
First published 2 September 2013

Lévy-like Distribution Shown by Intermittent Search Model with Misunderstanding Switch Pattern

Hisashi Murakami, Yukio Gunji


In an intermittent random search, in which slow motion to detect the target is discretely separated from the motion to migrate to another feeder, the high efficiency of the Lévy strategy is generally found, meaning that the time interval of phase switching is chosen from the Lévy distribution. Though the Lévy strategy is consistent with the searching behavior of real animals, some researchers claim that the Lévy-like distributions exhibited by animals are not necessarily produced by a Lévy process. Here, we propose an intermittent two-phase search model that does not include a Lévy process. In this model, the agent is basically a correlated random walker (CRW), but it memorizes its trajectory and counts the number of crossovers in a trajectory. If the number exceeds a threshold, the agent resets the memory of trajectories and makes ballistic movement in the direction uncorrelated to the past. We also show that this model can optimize the trade-off between macro search (exploration) and micro search (exploitation), which is shown by the CRW. Finally, we demonstrate that another intermittent search model that uses an ambiguous rule to switch the two phases can show a Lévy-like distribution of time intervals.