Cucker-Smale Flocking Under Hierarchical Leadership and Random Interactions

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. Mailing address: Centro de Matemática, Facultad de Ciencias, Iguá 4225, 11400, Montevideo, Uruguay. Telephone number: 598 2 5252522, E-mail: [email protected], Fax number: 598 2 5220653. Mailing address: Centro de Matemática, Facultad de Ciencias, Iguá 4225, 11400, Montevideo, Uruguay. Telephone number: 598 2 5252522, E-mail: [email protected], Fax number: 598 2 522 06 53.