相关论文: Synchrony and Anti-Synchrony for Difference-Couple…

The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in…

Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…

A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…

The structure of the graph defined by the interactions in a Boolean network can determine properties of the asymptotic dynamics. For instance, considering the asynchronous dynamics, the absence of positive cycles guarantees the existence of…

The analysis of the dynamics on complex networks is closely connected to structural features of the networks. Features like, for instance, graph-cores and node degrees have been studied ubiquitously. Here we introduce the D-spectrum of a…

We introduce the concept of a semigroup coupled cell network and show that the collection of semigroup network vector fields forms a Lie algebra. This implies that near a dynamical equilibrium the local normal form of a semigroup network is…

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

We present a general information theoretic approach for identifying functional subgraphs in complex networks where the dynamics of each node are observable. We show that the uncertainty in the state of each node can be expressed as a sum of…

There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…

This paper proposes a dynamic sensor scheduling method for sensor networks. In sensor network applications, we often need multiple equally-informative node subsets that are activated sequentially to make a sensor network robust against…

In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically and experimentally how the degree of the nodes through which two networks are…

We explore the concept of separating systems of vertex sets of graphs. A separating system of a set $X$ is a collection of subsets of $X$ such that for any pair of distinct elements in $X$, there exists a set in the separating system that…

Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…

The stability (or instability) of synchronization is important in a number of real world systems, including the power grid, the human brain and biological cells. For identical synchronization, the synchronizability of a network, which can…

This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. In particular, we are interested in…

The core vertex set of a graph is an invariant of the graph. It consists of those vertices associated with the non-zero entries of the nullspace vectors of a $\{0,1\}$-adjacency matrix. The remaining vertices of the graph form the…

We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular…

Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network…

In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms''…

We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…