Motivated by recent experimental and computational results that
show a motility-induced clustering transition in self-propelled particle systems,
we study an individual model and its corresponding Self-Organized Hydrodynamic
model for collective behaviour that incorporates a density-dependent
velocity, as well as inter-particle alignment. The modal analysis of the hydrodynamic
model elucidates the relationship between the stability of the equilibria
and the changing velocity, and the formation of clusters. We find, in agreement
with earlier results for non-aligning particles, that the key criterion for stability
is (ρv(ρ))0 ≥ 0, i.e. a nondecreasing mass flux ρv(ρ) with respect to the density.
Numerical simulation for both the individual and hydrodynamic models
with a velocity function inspired by experiment demonstrates the validity of
the theoretical results.