## Abstract

Along the lines of a previous paper (Seno [2]), making use of an intuitive model, we consider mathematically the relation between the efficiency of searcher's two-mode searching behavior and the target's patchy distribution, and discuss the strategic adaptability of two-mode searching. In this paper, the model is constructed by a time-discrete stochastic process on S^{1}, that is, on a circle. It can be regarded as a modification of Model 2 analyzed in Seno [2]. Differently from Model 2, the searcher's present location is assumed to be influenced by the past passage configuration. This modification yields some particular results for the present model. Also in the present model, if the patch size becomes sufficiently small, a two-mode searching behavior is strategically adaptable for the searcher. In this model, two-mode searching behavior has high strategic adaptability. Moreover, two-mode searching with an outstanding behavior change is strategically rather adaptable. As for the target's distribution, it appears that a particular patchy distribution is likely to be adopted, depending on the searcher's searching strategy. This result obviously indicates that the target's distribution may be adopted as its evolutionary strategy against the searcher, like a relation between a patchy distributed prey and its predator.

Original language | English |
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Pages (from-to) | 505-523 |

Number of pages | 19 |

Journal | Japan Journal of Industrial and Applied Mathematics |

Volume | 8 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1991 Oct |

Externally published | Yes |

## Keywords

- Markov chain
- mathematical model
- searching

## ASJC Scopus subject areas

- Engineering(all)
- Applied Mathematics