On Flocks Under Switching Directed Interaction Topologies

We prove unconditional and conditional flocking results for a Cucker--Smale flocking model enhanced with switching topologies. These topologies can be arbitrary; in particular, they are not necessarily symmetric. Our proofs hold for both discrete and continuous time. In both cases, the critical exponent discriminating between unconditional and conditional flocking is shown to be at most $\frac{1}{2(k-1)}$, where $k$ is the number of agents in the population.