Group Chase and Escape with Conversion from Targets to Chasers

TL;DR

This paper investigates how converting caught targets into new chasers affects group chase and escape dynamics, revealing optimal conditions for maximum target lifetime through numerical simulations.

Contribution

It introduces and analyzes the combined effects of target-to-chaser conversion and self-multiplying abilities on chase dynamics, a novel approach in this problem domain.

Findings

Conversion reduces target lifetimes significantly.

Existence of a maximum lifetime at specific initial target numbers.

Optimal combination of conversion and self-multiplying extends target survival.

Abstract

We are studying the effect of converting caught targets into new chasers in the context of the recently proposed `group chase and escape' problem. Numerical simulations have shown that this conversion can substantially reduce the lifetimes of the targets when a large number of them are initially present. At the same time, it also leads to a non-monotonic dependence on the initial number of targets, resulting in the existence of a maximum lifetime. As a counter effect for this conversion, we further introduce self-multiplying abilities to the targets. We found that the longest lifetime exists when suitable combination of these two effects is created.