Swarming of multi-agents with topological-based random interaction

In a recent PNAS article, Ballerini et al. provided evidence that birds in flocks interact with a fixed number of nearest neighbors, rather than with all neighbors within a fixed metric distance, as most previous models assumed. They also conducted numerical simulations to show that interacting with a fixed number of nearest neighbors achieved significantly higher cohesion of the aggregation compared with a standard metric one. In this paper, we propose a topological flocking model which introduce uncertainty into the nearest neighbor choice in the sense that the probability of an agent to be a neighbor of another one depends on their distance. We find that the agents are more prone to achieve flocking under a higher randomness of neighbor selection and a larger number of neighbors. The upper bound of the probability parameter which is negative correlation with randomness is derived by a statistical method.