Cucker-Smale Flocking Under Hierarchical Leadership and Random Interactions

TL;DR

This paper extends the Cucker-Smale flocking model to include hierarchical leadership and random interactions, demonstrating that flocking behavior persists despite probabilistic failures in perception among birds.

Contribution

It introduces a stochastic version of the hierarchical Cucker-Smale model and proves flocking still occurs under random interaction failures.

Findings

Flocking persists despite probabilistic perception failures.

Hierarchical structure influences velocity alignment.

Random interactions do not prevent flocking.

Abstract

Consider a flock of birds that fly interacting between them. The interactions are modelled through a hierarchical system in which each bird, at each time step, adjusts its own velocity according to his past velocity and a weighted mean of the relative velocities of its superiors in the hierarchy. We consider the additional fact, that each of the birds can fail to see any of its superiors with certain probability, that can depend on the distances between them. For this model with random interactions we prove that the flocking phenomena, obtained for similar deterministic models, holds true.