Cucker–Smale Flocking Under Hierarchical Leadership and Random Interactions

Source abstract

Consider a flock of birds that fly interacting between them. This flock is a hierarchical system in which each bird, at each time step, adjusts its own velocity according to its past velocity and a linear combination of the relative velocities of its superiors in the hierarchy. This linear combination has nonnegative random coefficients, including the case in which each of the birds can fail to see any of its superiors with certain probability. For this model with random interactions we prove that the flocking results, obtained for similar deterministic models, hold true.