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Some mathematical considerations on two-mode searching I

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Abstract

Purpose of this paper is to consider mathematically the relation between the efficiency of two-mode searching behavior and the target’s patchy distribution. Two-mode searching includes patch-searching and target-catching. Two intuitive models are presented: Model 1 constructed by a Wiener process onR 1; Model 2 by a time-discrete Markov process onS 1, that is, on a circle. These two different models give different results depending on the characteristics of each model. We apply our results to a coevolutionary game between the searcher’s searching behavior and the target’s distribution. Compared with a simple mode searching, the superiority of two-mode searching is shown to depend seriously on the target’s distribution.

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Seno, H. Some mathematical considerations on two-mode searching I. Japan J. Indust. Appl. Math. 8, 325 (1991). https://doi.org/10.1007/BF03167685

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  • DOI: https://doi.org/10.1007/BF03167685

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