The paper applies linear cyclic pursuit strategy to control mobile agents so as to cover an annular region efficiently, effectively, and safely. Cyclic pursuit strategy is considered as the minimalism in networked control since only one-way communication is used. Despite its simplicity, this strategy is shown to be capable of generating a class of epicyclic trajectories that have some advantages in dynamic coverage control. In the paper, the distributed coverage control strategy is presented, performance metrics in spatial and temporal domains are analyzed, and safety criteria for collision avoidance are established. The proposed approach should shed light on the design of mobile agents in dynamic coverage.