On the control of a flock by a leader

The collective and individual behaviors of the elements of a set of identical units are investigated from the point of view of their response to a coordination signal broadcast by a leader. In terms of the model used here, we show that for such systems nonlinearity plays a critical role. A new method for establishing controllability of nonlinear, replicated systems is given. Similarly, stabilization also depends on high order nonlinear effects. For the purpose of stabilization, a distinction between odd order nonlinear terms and even order nonlinear terms plays a role.