Modeling, analysis, and optimization of three-dimensional restricted visual field metric-free swarms

Models have proven useful in revealing the mechanisms underlying these collective behaviors of flocks of birds, schools of fish, swarms of insects, and herds of mammals. Biologists have found that the interaction among the starlings depends on topological rather than metric distance. Most of these topology-based collective models endow single particle with a global visual field, in order to provide each particle with sufficient information about the surroundings. However, in nature, the individual in a group usually has a restricted visual field, such as the visual field of starlings is 143∘. In this paper, we mainly investigate whether a global visual field is necessary to form a consistent and cohesive group in swarms. In order to solve this problem, we propose a three-dimensional restricted visual field metric-free(RVFMF) model based on Pearce and Turner’s previous work. Furthermore, we discuss several vital factors governing the convergent consistency of the RVFMF model with the assistance of extensive numerical simulations. According to the simulation results, we conclude that the best view angle of each particle in a swarm increases with increasing population size. Besides, the best view angle gradually becomes stable around 155∘ when the population size is larger than 1000. We also present data from quantitative analysis to prove that a flock of birds could obtain better coordination pattern under an optimal restricted visual field rather than under a global visual field.