Onset of order in the Vicsek-Kuramoto model with generalized noise

Complex systems where the constituents are subject to alignment interactions can be found across the scales in Nature, ranging from small biological systems to social behavior on larger scales. Such systems are inevitably also subject to various sources of noise, originating either from external perturbations or internal mechanisms. In active matter systems where alignment leads to swarming behavior the noise typically represent some degree of imperfection in the alignment rule. However, it may also be beneficial to model more complex behavioral patterns as stochastic terms in the equations of motion, like sudden changes in the direction of motion which is not captured by standard Gaussian white noise. By studying a system of self-propelled particles aligning through a Kuramoto interaction, we show that for a large class of noise types the onset of order takes place at a critical interaction timescale that is related to the persistence time of the active system in the non-interacting limit. We consider a special case of Poissonian noise representing abrupt directional changes and study the resulting collective behavior in the partially ordered state right after the transition point.