逃避猎物的生存
Survival of an evasive prey
摘要：
我们研究被N个捕食者捕食的猎物的生存。捕食者执行独立的随机行走在一个正方形格子与V网站，并开始直接追逐时，猎物出现在他们的视线范围内。当捕食者跳到猎物所占据的位置时，猎物就被抓住了。我们分析了一个懒惰的，最小的努力逃避策略的有效性，根据该策略，猎物试图避免遇到捕食者，使一跳，只有当任何捕食者出现在其视线范围内，否则猎物保持静止。我们表明，如果这样一个懒惰的猎物的视线范围是等于1格间距，至少需要3个捕食者，以赶上猎物的正方形格子。在这种情况下，我们建立了一个简单的渐近关系ln（Pev）（t）\sim（N/V）2ln（Pimm（t））之间的生存概率逃避和不动的猎物。因此，当捕食者密度较低（N/V<<1）时，懒惰逃避策略导致生存概率的显著增加。我们还认为，一个短视的猎物（它的视线范围小于捕食者的视线范围）经历了有效的superdiffusive运动，由于它遇到的捕食者，而一个远视的猎物进行扩散型运动。
英文摘要：
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 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
