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The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given…
Where graphs are used for modelling and specifying systems, consistency is an important concern. To be a valid model of a system, the graph structure must satisfy a number of constraints. To date, consistency has primarily been viewed as a…
The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on…
This paper presents a formal definition of stability for node centrality measures in weighted graphs. It is shown that the commonly used measures of degree, closeness and eigenvector centrality are stable whereas betweenness centrality is…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, learning…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
The stability method is very useful for obtaining exact solutions of many extremal graph problems. Its key step is to establish the stability property which, roughly speaking, states that any two almost optimal graphs of the same order $n$…
We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
Graph processing has become an important part of various areas of computing, including machine learning, medical applications, social network analysis, computational sciences, and others. A growing amount of the associated graph processing…
Graph neural networks (GNNs) are learning architectures that rely on knowledge of the graph structure to generate meaningful representations of large-scale network data. GNN stability is thus important as in real-world scenarios there are…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
Graphs are widespread data structures used to model a wide variety of problems. The sheer amount of data to be processed has prompted the creation of a myriad of systems that help us cope with massive scale graphs. The pressure to deliver…
A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
In this letter, we perform a sensitivity analysis on the master stability function approach for the synchronization of networks of coupled dynamical systems. More specifically, we analyze the linear stability of a nearly synchronized…