Robustness of optimal intermittent search strategies in dimension 1, 2 and 3

TL;DR

This paper systematically analyzes optimal intermittent search strategies across one, two, and three dimensions, demonstrating their robustness and providing detailed models and results applicable to various real-world search problems.

Contribution

It offers a comprehensive, systematic analysis of optimal intermittent search strategies in multiple dimensions, including new modeling of detection phases and robustness results.

Findings

Optimal search strategies minimize detection time across dimensions.

Robustness of strategies is independent of detection phase modeling.

Provides detailed calculations for different hypotheses and dimensions.

Abstract

Search problems at various scales involve a searcher, be it a molecule before reaction or a foraging animal, which performs an intermittent motion. Here we analyze a generic model based on such type of intermittent motion, in which the searcher alternates phases of slow motion allowing detection, and phases of fast motion without detection. We present full and systematic results for different modeling hypotheses of the detection mechanism in space dimension 1, 2 and 3. Our study completes and extends the results of our recent letter [Loverdo {\it et al.} Nature Physics {\bf 4}, 134 (2008)] and gives the necessary calculation details. In addition, a new modeling of the detection phase is presented. We show that the mean target detection time can be minimized as a function of the mean duration of each phase in dimension 1, 2 and 3. Importantly, this optimal strategy does not depend on the details of the modeling of the slow detection phase, which shows the robustness of our results. We believe that this systematic analysis can be used as a basis to study quantitatively various real search problems involving intermittent behaviors.