  We study synchronization for linearly coupled temporal networks of
heterogeneous time-dependent nonlinear agents via the convergence of attracting
trajectories of each node. The results are obtained by constructing and
studying the stability of a suitable linear nonautonomous problem bounding the
evolution of the synchronization errors. Both, the case of the entire network
and only a cluster, are addressed and the persistence of the obtained
synchronization against perturbation is also discussed. Furthermore, a
sufficient condition for the existence of attracting trajectories of each node
is given. In all cases, the considered dependence on time requires only local
integrability, which is a very mild regularity assumption. Moreover, our
results mainly depend on the network structure and its properties, and achieve
synchronization up to a constant in finite time. Hence they are quite suitable
for applications. The applicability of the results is showcased via several
examples: coupled van-der-Pol/FitzHugh-Nagumo oscillators, weighted/signed
opinion dynamics, and coupled Lorenz systems.
