Proceedings of the National Academy of Sciences, 2009
We study the survival of a prey that is hunted by N predators. The predators perform independent ... more 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 P ev ( t ) ∼ ( N / V ) 2 ln P imm ( t ) between the survival probabilities of an evasive and an immobile prey. Hence, when the density ρ = N / V of the predators is low, ρ ≪ 1, the lazy evasion strategy leads to the...
Proceedings of the National Academy of Sciences, 2009
We study the survival of a prey that is hunted by N predators. The predators perform independent ... more 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 P ev ( t ) ∼ ( N / V ) 2 ln P imm ( t ) between the survival probabilities of an evasive and an immobile prey. Hence, when the density ρ = N / V of the predators is low, ρ ≪ 1, the lazy evasion strategy leads to the...
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