Group chase and escape with conversion from targets to chasers

Abstract

We study 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 a suitable combination of these two effects is created.