We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent 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.

This is a joint work with Hildeberto Jardon-Kojakhmetov (University of Groningen) and Christian Kuehn (Technische Universität München)