Enhancing the network synchronizability

Abstract

The structural and dynamical properties, particularly the small-world effect and scale-free feature, of complex networks have attracted tremendous interest and attention in recent years. This article offers a brief review of one focal issue concerning the structural and dynamical behaviors of complex network synchronization. In the presentation, the notions of synchronization of dynamical systems on networks, stability of dynamical networks, and relationships between network structure and synchronizability, will be first introduced. Then, various technical methods for enhancing the network synchronizability will be discussed, which are roughly divided into two classes: Structural Modification and Coupling-Pattern Regulation, where the former includes three typical methods--dividing hub nodes, shortening average distances, and deleting overload edges, while the latter mainly is a method of strengthening the hub-nodes' influence on the network.

IEEE Transactions on Control of Network Systems information for authors

“…Hence, the edge weights can be adapted by steepest descent, also in a decentralized fashion and satisfying the feasibility constraints, using Equations (6), (9) and (10) where the term ∂f (w) ∂wi,j is replaced by its corresponding estimate according to Equation (27) or Equation (29). For Equation (27), this also requires the use of two additional layers, the Proportional-Integral (PI) Consensus layer and the λ 2 -Estimator layer as in Equations (11)- (15).…”

“…Again, weight adaptation is controlled using the estimated sensitivity from Equation (6), where the partial derivative of the modified objective function is given by Equation (10) to account for the multiple q i,j which grow according to Equation (9). The interplay of these equations is summarized in the schematic diagram shown in Figure 3.…”

“…As a representative problem we choose that of making the network achieve optimal synchronizability, that is, a configuration allowing its nodes to synchronize with maximal range of coupling gains (see [6]- [9] for further details). As discussed in previous work (e.g.…”

“…As discussed in previous work (e.g. [9]- [11]), maximal synchronizability can be achieved by maximizing the algebraic connectivity λ 2 , the second smallest eigenvalue of the graph Laplacian, or by minimizing the eigenratio r = λ n /λ 2 , with λ n being the largest Laplacian eigenvalue. We add some constraints to model the realistic case of each agent having a limited communication bandwidth.…”

Modeling mobile ad hoc communication networks on two-dimensional square lattice

“…A complex network can be developed by nodes representing individuals in a real system and by links representing interactions between them. Topological effects on dynamic behaviors in a network such as synchronization [3][4][5] and epidemic spreading [6] have been investigated widely. Most previous study on the complex networks focuses on topological properties of them ignoring the geometric distance between nodes, which is reasonable for some networks such as food web [7], citation networks [8], metabolic networks [9] etc.…”