期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2009
卷号：106
期号：33
页码：13696-13701
DOI：10.1073/pnas.0904354106
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：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 lnP ev(t) [~] (N/V)2lnP imm(t) between the survival probabilities of an evasive and an immobile prey. Hence, when the density {rho} = N/V of the predators is low, {rho} << 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.
关键词：pursuit ; chase ; diffusion ; superdiffusion ; first-passage times
