Flocking at the edge of chaos

Recent investigations have provided important insights into the complex structure and dynamics of collectively moving flocks of living organisms. Two intriguing observations are, scale-free correlations in the velocity fluctuations, in the presence of a high degree of order, and topological distance mediated interactions. Understanding these features, especially, the origin of fluctuations, appears to be challenging in the current scheme of models. It has been argued that flocks are poised at criticality. We present a self-propelled particle model where neighbourhoods and forces are defined through topology based rules. The force fluctuations occur spontaneously, and gives rise to scale-free correlations in the absence of noise and in the presence of alignment of velocities. We characterize the behaviour of the model through power spectral densities and the Lyapunov spectrum. Our investigations suggest self-organized criticality as a probable route to the existence of criticality in flocks.