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 on R1; Model 2 by a time-discrete Markov process on S1, 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.

Original languageEnglish
Pages (from-to)325-344
Number of pages20
JournalJapan Journal of Industrial and Applied Mathematics
Volume8
Issue number2
DOIs
Publication statusPublished - 1991 Jun 1
Externally publishedYes

Keywords

  • Markov process
  • Wiener process
  • mathematical model
  • searching

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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