Dynamic Consensus under Weak Coupling: a case study of nonlinear oscillators

Dynamic consensus is a term coined in1 [1] to denote the state of synchronization of complex networked systems. It covers the common paradigm of consensus in which case all the systems stabilize at a common equilibrium point. It is known that for certain networks (e.g., of homogeneous systems) dynamic consensus is achievable provided the interconnection gain is elevated. In this case, all the systems behave as one average dynamical system. In this paper we analyze the collective behavior of heterogeneous Stuart-Landau oscillators under weak coupling. We show that their behavior cannot be characterized by a single average system, but by a reducedorder network. We give a detailed characterization of the latter and establish a relation with the eigenvalues of the underlying Laplacian matrix, hence, with the network's topology.