Aggregation Strategies In Group Chase And Escape Model Increase The Survival Time Of Prey

There are many fascinating phenomenon in nature and collective behavior is one of them. Itembodies the wonderful essence of collective behaviors, such as the division of labor and collab-oration in ant colonies and the navigation behaviors in bird flocks. In recent years many simpleinteraction models based on agents were proposed by scientists to simulate collective behaviors.Related macroscopic phenomenon emerges in these models, as the result of the simple interac-tion rules among the agents in these models. One category of these model, called the chase andescape model, is very interesting. The chase and escape models concern the predation and otherpursuit-and-evasion problems. These models consist of many versions, including models basedon discrete lattice and continuous space, with1prey vs.1predator,1prey vs. M predators and Nprey vs. M predators. Pursuit-and-evasion problems are so widely studies, not only because of thesignificance in theory, that simple rules can produce complex emergent macroscopic phenomenonand the emergence exists universally in complex systems, but also because of the widespread po-tential applications, such as automatic formation for UAVs, launch and defense of missiles, andthe realization of individual autonomies to reduce the cost of centralized control. From our ob-servation of nature, and the researches on animal aggregation behaviors in ecology, aggregationalways brings direct and indirect benefits to the animal groups, no matter whether they are awareof it.Thus we propose several aggregation strategies and study how aggregation impacts on sur-vival time of prey by introducing the strategies into the group chase and escape model with N preyvs. M predators. Firstly, we develop the model based on discrete lattice by introducing three ag-gregation strategies. By comparison with the original model without aggregation, the results showthat aggregation strategies dramatically increase the group survival time of prey, even makingpredators disable to complete the entire catch in a relative long period of time. We also analyzethe average survival time of prey and find that the average survival time τ and the aggregation probability P have power-law dependence for P∈[0.9,0.997]. As the number of predators de-creases, there is still a phase transition in the increase of the average survival time for prey, with thephase transition point staying the same as the original model. The phase transition point is the bestratio of predators and prey for the predatory efciency. With a fixed number of prey, the averagesurvival time increases significantly when the number of predators is less than the critical pointvalue due to aggregation; when the number is greater than the critical point value, aggregationhas no efects on the average survival time. Secondly, we introduce an aggregation strategy intothe continuous space model and draw similar conclusions by comparison with the lattice model.Aggregation dramatically increases the group survival time without uncompleted catch runs. Andthe average survival time τ and the predators number M also have power-law dependence. In thefigure of the average survival time against the number of predators, there is still a phase transition,while the critical point has changed.Sharing the information of escaping routes among prey during the aggregation process leadsthe system components form a relatively steady alignment state. This is the main reason to extendthe group survival time of prey. This paper demonstrates and elaborates the aggregation andpursuit-and-evasion behaviors in biological systems from another perspective. We hope to providesome useful ideas to the future researches and applications on collective behaviors.