On practical synchronization of heterogeneous networks of nonlinear systems: application to chaotic systems

We employ stability theory to study the problem of synchronization of networked heterogeneous systems. Typically, for the case of homogeneous networks, this comes to analyzing the stability and attractivity of a synchronization manifold. In the case of heterogeneous networks, the synchronization manifold does not necessarily exist. Instead, we show that an average dynamics emerges, to which the dynamics of all nodes in the networks converge in a practical sense. More precisely, under the assumption that the emergent dynamics has an attractor one can establish that the nodes synchronize in a practical sense, that is, their motions approach the attractor of the emergent dynamics and remain close to it.