Group chase and escape with conversion from targets to chasers

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.

Chasing and escaping by three groups of species

“…The motion of each particle is similar to that in Refs. [8,9]. In one trial, we choose one of the particles and move the particle.…”

“…When the area in which the target searches for the chasers is wider than the area in which the chasers search for the target, the time dependence changes from t to t 1.65 . Recently, Kamimura and co-workers used a simple model and studied group chase and escape [8][9][10]. In the studies, the system consists of two types of species: one is a group of chasers, which try to catch the nearest target, and the other is a group of targets, which escape from the nearest target.…”

“…The models are simplified and generalized, so that they can be regarded as the basic models of the motions of interacting entities such as human societies, animals, and bacteria. One model in previous studies about group chase and escape [8][9][10] is one of those simplified and generalized models, so that it may be applied to many problems. Thus, it is useful to expand the model and to study basic properties.…”

“…In previous studies [8][9][10], the system consisted of two types of species, namely targets and chasers. In this paper, we consider a system formed by three species: particles in one * sato@cs.kanazawa-u.ac.jp species act as chasers for another species and as targets for the third species.…”

Group chase and escape with some fast chasers

“…For * sato@cs.s.kanazawa-u.ac.jp example, Nishi and coworkers studied the group chase and escapes under a conversion law [9], and we studied the group chase and escape with three species [10]. In the previous paper [8], some variations of the original model, which are valuable to study, are suggested.…”