Effective dynamics for chaos synchronization in networks with time-varying topology

A coupled map lattice whose topology changes at each time step is studied. We show that the transversal dynamics of the synchronization manifold can be analyzed by the introduction of effective dynamical quantities. These quantities are defined as weighted averages over all possible topologies. We demonstrate that an ensemble of short time observations can be used to predict the long-term behavior of the lattice. Finally, we point out that it is possible to obtain a lattice with constant topology in which the dynamical behavior is asymptotically identical to one of the time-varying topology.

► There is equivalence between the time-varying topology and a constant static one.
► Effective quantities are given by weighted averages over all possible topologies.
► The effective coupling matrix is obtained from the effective coupling eigenvalues.
► The transition to synchronization for both systems occurs at the same parameters set.