Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization.
Collective motion of self-propelled agents has attracted much attention in vast disciplines. However, almost all investigations focus on such agents evolving in the Euclidean space, with rare concern of swarms on non-Euclidean manifolds. Here we present a novel and fundamental framework for agents evolving on a sphere manifold, with which a variety of concrete cooperative-rules of agents can be designed separately and integrated easily into the framework, which may perhaps pave a way for considering general spherical collective motion (SCM) of a swarm. As an example, one concrete cooperative-rule, i.e., the spherical direction-alignment (SDA), is provided, which corresponds to the usual and popular direction-alignment rule in the Euclidean space. The SCM of the agents with the SDA has many unique statistical properties and phase-transitions that are unexpected in the counterpart models evolving in the Euclidean space, which unveils that the topology of the sphere has an important impact on swarming emergence.
Department of Control and Systems Engineering, Nanjing University, China.
Wei
W
Li