  In this paper, we study the synchronization of identical Kuramoto phase
oscillators under cumulative stochastic damage to the edges of networks. We
analyze the capacity of coupled oscillators to reach a coherent state from
initial random phases. The process of synchronization is a global function
performed by a system that gradually changes when the damage weakens individual
connections of the network. We explore diverse structures characterized by
different topologies. Among these are deterministic networks as a wheel or the
lattice formed by the movements of the knight on a chess board, and random
networks generated with the Erd\H{o}s-R\'enyi and Barab\'asi-Albert algorithms.
In addition, we study the synchronization times of 109 non-isomorphic graphs
with six nodes. The synchronization times and other introduced quantities are
sensitive to the impact of damage, allowing us to measure the reduction of the
capacity of synchronization and classify the effect of damage in the systems
under study. This approach is general and paves the way for the exploration of
the effect of damage accumulation in diverse dynamical processes in complex
systems.
