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Survival of an evasive prey | | G. Oshanin
; O. Vasilyev
; P. L. Krapivsky
; J. Klafter
; | | Date: |
8 Sep 2009 | | Abstract: | We study the survival of a prey that is hunted by N predators. The predators
perform independent random walks on a square lattice with V sites and start a
direct chase whenever the prey appears within their sighting range. The prey is
caught when a predator jumps to the site occupied by the prey. We analyze the
efficacy of a lazy, minimal-effort evasion strategy according to which the prey
tries to avoid encounters with the predators by making a hop only when any of
the predators appears within its sighting range; otherwise the prey stays
still. We show that if the sighting range of such a lazy prey is equal to 1
lattice spacing, at least 3 predators are needed in order to catch the prey on
a square lattice. In this situation, we establish a simple asymptotic relation
ln(Pev)(t) sim (N/V)2ln(Pimm(t)) between the survival probabilities of an
evasive and an immobile prey. Hence, when the density of the predators is low
N/V<<1, the lazy evasion strategy leads to the spectacular increase of the
survival probability. We also argue that a short-sighting prey (its sighting
range is smaller than the sighting range of the predators) undergoes an
effective superdiffusive motion, as a result of its encounters with the
predators, whereas a far-sighting prey performs a diffusive-type motion. | | Source: | arXiv, 0909.1445 | | Services: | Forum | Review | PDF | Favorites | |
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