  We analyze the final state sensitivity of nonlocal networks with respect to
initial conditions of their units. By changing the initial conditions of a
single network unit, we perturb an initially synchronized state. Depending on
the perturbation strength, we observe the existence of two possible network
long-term states: (i) The network neutralizes the perturbation effects and
returns to its synchronized configuration. (ii) The perturbation leads the
network to an alternative desynchronized state. By computing uncertainty
exponents of a two-dimensional cross section of the state space, we find the
existence of fractal basin boundaries separating synchronized solutions from
desynchronized ones. We attribute these features to an unstable chaotic set in
which trajectories persist for times indefinitely long in the network.
