Portraits of cyclic pursuit

The study of cyclic pursuit as a means to collective behavior in nature and in artificial multi-agent systems is of current interest. Here we examine the nonlinear closed loop dynamics of planar cyclic pursuit based on the constant bearing (CB) strategy. We show that there exists a family of rectilinear relative equilibria that admit nearby periodic orbits in an appropriate low dimensional space found by methods of symmetry, reduction and constraint. We also demonstrate the existence of other families of rectilinear equilibria that exhibit attractivity or instability.