Spontaneous fluctuations in a zero-noise model of flocking

¹ The Institute of Mathematical Sciences, CIT Campus - Taramani, Chennai 600113, India
² Department of Information and Computer Science, Aalto University - P.O. Box 15400, FI-00076, Finland

Received: 9 August 2016
Accepted: 5 December 2016

Abstract

Investigations into the complex structure and dynamics of collectively moving groups of living organisms have provided valuable insights. Understanding the emergent 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 two-dimensional self-propelled particle model where neighbourhoods and forces are defined through topology-based rules. The attractive forces are modeled in order to maintain cohesion in the flock in open-boundary conditions. We find that fluctuations occur spontaneously in the absence of any external noise. For certain values of the parameters the flock shows a high degree of order as well as scale-free decay of spatial correlations in velocity and speed. We characterize the dynamical behaviour of the system using the Lyapunov spectrum. Largest exponents being positive but small in magnitude suggest that the apparent high susceptibility may result from the system operating near the borderline of order and chaos.