  In this work we derive and analyze coarse-grained descriptions of
self-propelled particles with selective attraction-repulsion interaction, where
individuals may respond differently to their neighbours depending on their
relative state of motion (approach versus movement away). Based on the
formulation of a nonlinear Fokker-Planck equation, we derive a kinetic
description of the system dynamics in terms of equations for the Fourier modes
of a one-particle density function. This approach allows effective numerical
investigation of the stability of possible solutions of the system. The
detailed analysis of the interaction integrals entering the equations
demonstrates that divergences at small wavelengths can appear at arbitrary
expansion orders.
  Further on, we also derive a hydrodynamic theory by performing a closure at
the level of the second Fourier mode of the one-particle density function. We
show that the general form of equations is in agreement with the theory
formulated by Toner and Tu.
  Finally, we compare our analytical predictions on the stability of the
disordered homogeneous solution with results of individual-based simulations.
They show good agreement for sufficiently large densities and non-negligible
short-ranged repulsion. Disagreements of numerical results and the hydrodynamic
theory for weak short-ranged repulsion reveal the existence of a previously
unknown phase of the model consisting of dense, nematically aligned filaments,
which cannot be accounted for by the present Toner and Tu type theory of polar
active matter.
