Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey

Details Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey

2004-10-18

arxiv.org/abs/cond-mat/0410449v1

JSTAT (2005) P02005

Physics

Condensed Matter

Statistical Mechanics

5 pages

Scientific paper

10.1088/1742-5468/2005/02/P02005

We consider a system of three random walkers (a `cheetah' surrounded by two `antelopes') diffusing in one dimension. The cheetah and the antelopes diffuse, but the antelopes experience in addition a deterministic relative drift velocity, away from the cheetah, proportional to their distance from the cheetah, such that they tend to move away from the cheetah with increasing time. Using the backward Fokker-Planck equation we calculate, as a function of their initial separations, the probability that the cheetah has caught neither antelope after infinite time.

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