相关论文: Balanced Hodge Laplacians Optimize Consensus Dynam…

Full synchronization of dynamical elements coupled via hypergraphs can be analyzed with the hypergraph projection onto dyadic matrices, but this is not sufficient for analyzing cluster synchronization. Here we develop the necessary…

Networks are often interconnected, with one system wielding greater influence over another. However, the effects of such asymmetry on self-organized phenomena (e.g., consensus and synchronization) are not well understood. Here, we study…

We study an optimal control problem aimed at achieving a desired tradeoff between the network coherence and communication requirements in the distributed controller. Our objective is to add a certain number of edges to an undirected…

The presence of higher-order interactions (simplicial complexes) in networks and certain types of multilayer networks has shown to lead to the abrupt first-order transition to synchronization. We discover that simplicial complexes on…

We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…

Hodge Laplacians have been previously proposed as a natural tool for understanding higher-order interactions in networks and directed graphs. Here we introduce a Hodge-theoretic approach to spectral theory and dimensionality reduction for…

We establish explicit operator norm bounds and essential self-adjointness criteria for discrete Hodge Laplacians on weighted graphs and simplicial complexes. For unweighted $d$-regular graphs we prove the universal estimate…

Reaching consensus among states of a multi-agent system is a key requirement for many distributed control/optimization problems. Such a consensus is often achieved using the standard Laplacian matrix (for continuous system) or Perron matrix…

Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to…

A network of coupled dynamical systems is represented by a graph whose vertices represent individual cells and whose edges represent couplings between cells. Motivated by the impact of synchronization results of the Kuramoto networks, we…

The processing of signals supported on non-Euclidean domains has attracted large interest recently. Thus far, such non-Euclidean domains have been abstracted primarily as graphs with signals supported on the nodes, though the processing of…

In social networks, interaction patterns typically change over time. We study opinion dynamics on tie-decay networks in which tie strength increases instantaneously when there is an interaction and decays exponentially between interactions.…

Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or…

In this paper, we propose matrix-scaled consensus algorithms for linear dynamical agents interacting over an undirected network. Under the proposed algorithms, the state vectors of all agents to asymptotically agree up to some matrix…

In this work we present novel results to the problem of the Hegselmann-Krause dynamics in networks obtained by an extensive study of the behavior of the standard order parameter sensitive to the onset of consensus: the normalized size of…

Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a…

Higher-order interaction networks are typically modeled using hypergraphs or simplicial complexes, where interactions explicitly involve more than two nodes. Here we demonstrate that effective higher-order dynamical constraints emerge…

This study develops an original and innovative matrix representation with respect to the information flow for networked multi-agent system. To begin with, the general concepts of the edge Laplacian of digraph are proposed with its algebraic…

The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models,…

Geometric realization of opinion is considered as a simplex and the opinion space of a group of individuals is a simplicial complex whose topological features are monitored in the process of opinion formation. The agents are physically…