Effectual leadership in flocks with hierarchy and individual preference

We study the emergent ocking behavior in a group of interacting particles following a Cucker-Smale type model with hierarchical leadership and individual effects. In this model, each individual adjusts its velocity to match that of its leaders and in meantime has a preferred acceleration if there is no local velocity consensus. We give some sufficient conditions on the range of parameters and initial configurations to have an effectual leadership, i.e., to guarantee the asymptotic convergence to a velocity agreement with the leader. To do this, we explore a special matrix norm for the ocking under hierarchical leadership.