Related papers: Synchrony patterns in Laplacian networks
We consider weighted coupled cell networks, that is networks where the interactions between any two cells have an associated weight that is a real valued number. Weighted networks are ubiquitous in real-world applications. We consider a…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
The dynamical behavior of networked complex systems is shaped not only by the direct links among the units, but also by the long-range interactions occurring through the many existing paths connecting the network nodes. In this work, we…
We show that the degree distributions of graphs do not suffice to characterize the synchronization of systems evolving on them. We prove that, for any given degree sequence satisfying certain conditions, there exists a connected graph…
There is a wealth of applied problems that can be posed as a dynamical system defined on a network with both attractive and repulsive interactions. Some examples include: understanding synchronization properties of nonlinear oscillator;,…
We analyze the synchronization dynamics of phase oscillators far from the synchronization manifold, including the onset of synchronization on scale-free networks with low and high clustering coefficients. We use normal coordinates and…
This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is…
Quantifying the relations (e.g., similarity) between complex networks paves the way for studying the latent information shared across networks. However, fundamental relation metrics are not well-defined between networks. As a compromise,…
We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we…
The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…
We report on some recent developments in the search for optimal network topologies. First we review some basic concepts on spectral graph theory, including adjacency and Laplacian matrices, and paying special attention to the topological…
In this paper, subgraphs and complementary graphs are used to analyze the network synchronizability. Some sharp and attainable bounds are provided for the eigenratio of the network structural matrix, which characterizes the network…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…
The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…
We study the properties and stability of networks with arbitrary Laplacian coupling. Classic approaches to studying networked systems require unrealistic assumptions, including homogeneous node dynamics, one-dimensional and undirected…
In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via…
In this paper, we investigate the controllability of a linear time-invariant network following a Laplacian dynamics defined on a threshold graph. In this direction, an algorithm for deriving the modal matrix associated with the Laplacian…
In this paper, the investigation is first motivated by showing two examples of simple regular symmetrical graphs, which have the same structural parameters, such as average distance, degree distribution and node betweenness centrality, but…
We show that a network can self-organize its structure in a completely distributed manner in order to optimize its synchronizability whilst satisfying the local constraints: non-negativity of edge weights, and maximum weighted degree of…