The Influence Of Finite Horizon On Collective Motion In Group Chase And Escape Model

Collective motion in populations as herds, ants, fish school, birds,bacteria, pedestrians, robots, and so on has drawn great attention of researchers from diverse fields in these years. It is fascinating that simple motions of entities at the microscopic scale can result in complex emergent behaviors at the macroscopic scale through interaction among them. Chase and escape is an interesting subject with long history. The simplest case, such as a merchant vessel pursued by a pirate ship, is that one chaser pursues one escaper. With years of development, many scenarios have been studied.Group chase and escape, recently proposed by Kamimura and Ohira in 2010, addressed the impacts of the multi-agents interactions on the chase and escape. In the model, the chasers pursue the nearest escapers,while the escapers try to escape from being caught by the nearest chasers. Vicsek rated this research highly in Nature:’Hunting in groups or gregarious prey is such a widespread phenomenon in the animal kingdom that it comes as a surprise that the first simple model of the process has only just been published’. Since then, many modified versions of the model were proposed.In previous works, both chasers and escapers were assumed to have global field of vision, which means that they can see all the other entities. Considering that entities in reality are subjected to a limited field of vision, we modify the model of group chase and escape in this essay by introducing narrow sight to chasers. Extended and modified,two search strategies, random-walk-strategy and relocation-strategy, are introduced for chasers when escapers are out of their fields of vision.There exist two regimes for the group lifetime of escapers when chasers adopting random-walk-strategy. In the narrow sight regime, the group lifetime is a decreasing function of chasers’ sight range. In the wide sight regime, the group lifetime stays at a constant when chasers adopting random-walk-strategy while increases with the sight range when chasers adopting relocation-strategy. The impacts of the two search strategies on group chase and escape are studied by investigating the lifetime distribution of all escapers and the dependence of the minimum lifetime on the number of chasers. We also find that, to reach the most efficient and the lowest energy cost chase for chasers, the ratio between the number of chasers and escapers stays at around 6 under random-walk-strategy. However, the energy cost monotonically increases with increasing the number of chasers and there is no existence of an optimal number of chasers when chasers under relocation-strategy.