Topologically induced swarming phase transition on a 2D percolated lattice

The emergence of collective motion, or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that occurs at multiple spatio-temporal scales. Swarms that occur in natural environments typically have to contend with spatial disorder such as obstacles that can hinder an individual's motion or can disrupt communication with neighbors. We study swarming agents, possessing both aligning and mutually avoiding repulsive interactions, in a 2D percolated network representing a topologically disordered environment. We numerically find a phase transition from a collectively moving swarm to a disordered gas-like state above a critical value of the topological or environmental disorder. For agents that utilize only alignment interactions, we find that the swarming transition does not exist in the large system size limit, while the addition of a mutually repulsive interaction can restore the existence of the transition at a finite critical value of disorder. We find there is a finite range of topological disorder where swarming can occur and that this range can be maximized by an optimal amount of mutual repulsion.