The main results also apply to a class of weighted and directed networks and are thus relevant to assess the effect of nonuniform connection weights on the synchronization of real-world networks .
Synchronization is a widespread phenomenon in distributed systems, with examples ranging from neuronal to technological networks .
Previous studies have shown that network synchronization is strongly influenced by the randomness [4, 5], degree (connectivity) distribution , correlations [7, 8], and distributions of directions and weights [9, 10] in the underlying network of couplings.
For concreteness, I focus on complete synchronization of identical dynamical units , which has served as a prime paradigm for the study of collective dynamics in complex networks.
In this case, the synchronizability of the network is determined by the largest and smallest nonzero eigenvalues of the coupling (Laplacian) matrix.
But what is the ultimate origin of these dependences?
In this paper, I show that these and other important effects in the dynamics of complex networks are ultimately controlled by a small number of network parameters.The results are illustrated using synchronization phenomena as a model process.Complex dynamical systems are high dimensional in nature.My principal result is that, for a wide class of complex networks, these eigenvalues are tightly bounded by simple functions of the weights and degrees in the network.The quantities involved in the bounds are either known by construction or can be calculated in at most ) operations even for the special case of undirected networks.Special issues on high profile hot-topics are requested.Contributions will be by open submission, coordinated via a conference or by invitation.This is achieved by exploring the fact that the quantities used to express the bounds have direct physical interpretation.This leads to conditions for the enhancement and suppression of synchronization in terms of physical parameters of the network.The problem of network design and the impact of the network structure on dynamics are considered in sections 4 and 5, respectively.Concluding remarks are incorporated in the last section.