  We study collective dynamical behavior of active particles with topological
interactions and directional reversals. Surprising phenomena are shown to
emerge as the interaction relaxation time is varied relative to the reversal
rate, such as spontaneous formation of collective chiral states due to phase
synchronization, and collective directional reversals in the presence of
confinement. The results have a direct relevance to modelling and understanding
collective reversals and synchronization phenomena in active matter.
