Transitions in a self-propelled-particles model with coupling of accelerations

We consider a three-dimensional, generalized version of the original self-propelled-particles (SPP) model for collective motion. By extending the factors influencing the ordering, we investigate the case when the movement of the SPPs depends on both the velocity and the acceleration of the neighboring particles, instead of being determined solely by the former one. By changing the value of a weight parameter s determining the relative influence of the velocity and the acceleration terms, the system undergoes a kinetic phase transition as a function of a behavioral pattern. Below a critical value of s the system exhibits disordered motion, while above it the dynamics resembles that of the SPP model. We show that the critical value of the strategy variable could correspond to an evolutionary optimum in the sense that the information exchange between the units of the system is maximal in this point.