FRONTIERS IN THE STUDY OF CHAOTIC DYNAMICAL SYSTEMS WITH OPEN PROBLEMS

Abstract

We study the network synchronizability in terms of its local dynamics and in terms of its global dynamics. In previous work we obtained some results about the synchronization interval, when we fix the graph underlying the network, i.e., the network connection topology and vary the dy- namic in the nodes and about the effect of some graph parameters on the synchronization interval, supposing that the local dynamics in the nodes is fixed. We present numerical simulations for several network types and some conjectures suggested by these simulations. In particular, we are interested in the effect of the clustering coefficient, the conductance and the clustering performance, on the network synchronizability.