Capture of the Lamb: Diffusing Predators Seeking a Diffusing Prey

TL;DR

This paper investigates the complex dynamics of predators and prey, modeled as diffusing particles in one dimension, providing exact solutions for small numbers of predators and large predator populations, but leaving the general case unsolved.

Contribution

It offers exact probabilistic solutions for predator-prey capture dynamics with small predator numbers and applies extreme statistics for large numbers, highlighting unresolved cases.

Findings

Exact solutions for small predator numbers

Extreme statistics approach for large predator populations

Unsolved case for three or more predators

Abstract

We study the capture of a diffusing "lamb" by diffusing "lions" in one dimension. The capture dynamics is exactly soluble by probabilistic techniques when the number of lions is very small, and is tractable by extreme statistics considerations when the number of lions is very large. However, the exact solution for the general case of three or more lions is still not known.