  In this paper, we present a model describing the collective motion of birds.
The model introduces spontaneous changes in direction which are initialized by
few agents, here referred as leaders, whose influence act on their nearest
neighbors, in the following referred as followers. Starting at the microscopic
level, we develop a kinetic model that characterizes the behaviour of large
flocks with transient leadership. One significant challenge lies in managing
topological interactions, as identifying nearest neighbors in extensive systems
can be computationally expensive. To address this, we propose a novel
stochastic particle method to simulate the mesoscopic dynamics and reduce the
computational cost of identifying closer agents from quadratic to logarithmic
complexity using a $k$-nearest neighbours search algorithm with a binary tree.
Lastly, we conduct various numerical experiments for different scenarios to
validate the algorithm's effectiveness and investigate collective dynamics in
both two and three dimensions.
