A minimal model of intermittent search in dimension two

We propose and analyse a model of bidimensional search processes, explicitly relying on the widely observed intermittent behaviour of foraging animals, which involves a searcher enjoying minimal orientational and temporal memory skills. We show analytically that, in the case of non-revisitable targets, intermittent strategies can minimize the search time, and therefore constitute real optimal strategies, as opposed to Levy flights strategy which are optimal only in the particular case of revisitable targets. Two representative modes of target detection are presented, and they allow us to determine which characteristics of the optimal strategy are robust and do not depend on the specific characteristics of detection mechanisms. In particular, our study tends to show that the optimal duration of the ballistic phase is a universal feature of bidimensional intermittent search strategies. Last, by comparing the results of our minimal model to systematic search strategies, we show that if temporal and orientational memory skills speed up the search, they do not change the order of magnitude of the search time.