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We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
Phase transitions constitute fundamental mechanisms underlying abrupt or qualitative changes in the collective dynamics of interacting units across a wide range of natural and engineered systems. In dynamical networks, such transitions lead…
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
Synchronization is a crucial phenomenon in many natural and artificial complex network systems. Applications include neuronal networks, formation control and coordination in robotics, and frequency synchronization in electrical power grids.…
We investigate the dynamics of a broad class of stochastic copying processes on a network that includes examples from population genetics (spatially-structured Wright-Fisher models), ecology (Hubbell-type models), linguistics (the utterance…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
In recent years networks have gained unprecedented attention in studying a broad range of topics, among them in complex systems research. In particular, multi-agent systems have seen an increased recognition of the importance of the…
We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition…
Adaptive networks are well-suited to perform decentralized information processing and optimization tasks and to model various types of self-organized and complex behavior encountered in nature. Adaptive networks consist of a collection of…
Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can…
Network dynamics offers critical insights into the behavior and evolution of complex systems. Here, we focus on the topological dynamics of networks to explore a unique process for reducing the average distance: topological compression. The…
This article studies the synchronization problem of complex dynamical networks. The impulsive control method is considered with a novel event-triggered pinning algorithm. Sufficient conditions on the network topology are obtained to ensure…
Dynamic networks, also called network streams, are an important data representation that applies to many real-world domains. Many sets of network data such as e-mail networks, social networks, or internet traffic networks are best…
We present a rigorous mathematical framework for analyzing dynamics of a broad class of Boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in Boolean network…
With an increasing amount of observations on the dynamics of many complex systems, it is required to reveal the underlying mechanisms behind these complex dynamics, which is fundamentally important in many scientific fields such as climate,…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
Diffusion dynamics in multiplex networks can model a diverse number of real-world processes. In some specific configurations of these systems, the super-diffusion phenomenon arises, in which the diffusion is faster in the multiplex network…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…