  Recently, we proposed a self-propelled particle model with competing
alignment interactions: nearby particles tend to align their velocities whereas
they anti-align their direction of motion with particles which are further away
[R. Grossmann et al., Phys. Rev. Lett. 113, 258104 (2014)]. Here, we extend our
previous numerical analysis of the high density regime considering low particle
densities too. We report on the emergence of various macroscopic patterns such
as vortex arrays, mesoscale turbulence as well as the formation of polar
clusters, polar bands and nematically ordered states. Furthermore, we study
analytically the instabilities leading to pattern formation in mean-field
approximation. We argue that these instabilities are well described by a
reduced set of hydrodynamic equations in the limit of high density.
