Survival of an evasive prey
Survival of an evasive prey
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DOI：
10.1073/pnas.0904354106
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发表时间：
2009-08-18
影响因子：
11.1
通讯作者：
Klafter, J.
中科院分区：
文献类型：
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作者：
Oshanin, G.;Vasilyev, O.;Klafter, J.
我们研究被 N 个捕食者猎杀的猎物的生存情况。捕食者在带有V位点的方格上进行独立随机行走，并在猎物出现在它们的视线范围内时开始直接追逐。当捕食者跳到猎物占据的地点时，猎物就会被捕获。我们分析了一种懒惰的、最小努力的逃避策略的有效性，根据该策略，只有当任何捕食者出现在其视线范围内时，猎物才会通过跳跃来避免与捕食者相遇；否则猎物就会保持静止。我们证明，如果这种懒惰猎物的瞄准范围等于 1 个格子间距，则至少需要 3 个捕食者才能捕获方形格子上的猎物。在这种情况下，我们在躲避和不动的猎物的生存概率之间建立了一个类似于 (N/V)(2) ln P-imm(t) 的简单渐近关系 lnP(ev)(t)。因此，当捕食者的密度 rho = N/V 较低时， rho
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) similar to (N/V)(2) ln P-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