Stability of the vortex phase in self-propelled swarm systems

We investigate the dynamic responses and stabilities of vortex states of self-propelled swarm systems to external uniform impulsive perturbing forces by using particle-based simulations. Perturbed vortices are observed to move along logarithmic spiral paths before recovering their original phases. However, above some critical impulse, the systems are observed to cross over to crystal phases and never return. We examine the critical impulsive perturbation as a measure of stability, which is found to increase with self-propelling strength and to decrease with aggregating force strength and alignment range values. In addition, a long-lasting state in which an asymmetric vortex revolves circularly is found to exist at the border between the vortex and the crystal phases. This phenomenon is similar to the unstable equilibrium in conservative systems. All those results are analyzed and discussed using the equation of motion with some approximations.