  This study examines the synchronization of three identical oscillators
arranged in an array and coupled by small impacts, wherein each oscillator
interacts solely with its nearest neighbor. The synchronized state, which is
asymptotically stable, is characterized by phase opposition among alternating
oscillators. We analyze the system using a non-linear discrete dynamical system
based on a difference equation derived from the iteration of a plane
diffeomorphism. We illustrate these results with the application to a system of
three aligned Andronov clocks, showcasing their applicability to a broad range
of oscillator systems.
