An Algorithmic Approach to Flocking Behavior: Reaching beyond Global Phases

We present a flocking model which is able to create a collective time-dependent
behavior (termed dynamic emergence in this work) which is seen to naturally occur in a group of hundreds of real birds. The model is based on the ideas of consensus and frustration, where consensus is a nonlinear topological averaging that drives the particles towards one of three unique phases, and frustration is a perturbation that pushes the particles beyond these simple phases. The nonlinearity merged with these two rules produces characteristics which go beyond the dynamic interplay of global phase transitions. The emergent results are interpreted in terms of global and local order parameters, and correlation functions. In this work, three consensus rules are considered namely metrical, topological, and fixed topological neighbors, while the frustration rule follows a simple U-turn. To elucidate the exchange of information among members of the flock, a network analysis is performed. In particular, a comparison between networks arosed in a consensus rule based on metrical, topological, and fixed topological neighbors interactions is made.