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.

翻译：研究通过各节点吸引轨迹的收敛性，分析了具有时变非线性智能体的线性耦合时变网络的同步问题。通过构造并研究合适的线性非自治问题（用于约束同步误差演化）的稳定性，获得了相关结果。本文同时探讨了整个网络和仅集群两种情形，并讨论了所得同步对扰动的持续性。此外，给出了各节点存在吸引轨迹的充分条件。在所有情形中，所考虑的时间依赖性仅需局部可积性，这是一种非常宽松的正则性假设。进一步地，我们的结果主要依赖于网络结构及其性质，并在有限时间内实现达常数精度的同步，因此非常适合实际应用。通过多个示例（耦合范德波尔/菲茨休-南云振荡器、加权/有符号意见动力学、耦合洛伦兹系统）展示了结果的适用性。