  Systems composed of interacting self-propelled particles (SPPs) display
different forms of order-disorder phase transitions relevant to collective
motion. In this paper we propose a generalization of the Vicsek model
characterized by an angular noise term following an arbitrary probability
density function, which might depend on the state of the system and thus have a
multiplicative character. We show that the well established vectorial Vicsek
model can be expressed in this general formalism by deriving the corresponding
angular probability density function, as well as we propose two new
multiplicative models consisting on a bivariate Gaussian and a wrapped Gaussian
distributions. With the proposed formalism, the mean-field system can be solved
using the mean resultant length of the angular stochastic term. Accordingly,
when the SPPs interact globally, the character of the phase transition depends
on the choice of the noise distribution, being first-order with an hybrid
scaling for the vectorial and wrapped Gaussian distributions, and second order
for the bivariate Gaussian distribution. Numerical simulations reveal that this
scenario also holds when the interactions among SPPs are given by a static
complex network. On the other hand, using spatial short-range interactions
displays, in all the considered instances, a discontinuous transition with a
coexistence region, consistent with the original formulation of the Vicsek
model.
