Some mathematical considerations on two-mode searching I
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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.
Key wordssearching mathematical model Wiener process Markov process
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