Related papers: Uniqueness of Equilibria in Interactive Networks
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…
In a network game, players interact over a network and the utility of each player depends on his own action and on an aggregate of his neighbours' actions. Many real world networks of interest are asymmetric and involve a large number of…
The balance between excitation and inhibition is crucial for neuronal computation. It is observed that the balanced state of neuronal networks exists in many experiments, yet its underlying mechanism remains to be fully clarified.…
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…
We propose a simple semi-discrete spatial model where rents, wages and the density of population in a city can be deduced from free-mobility and equilibrium conditions on the labour and residential housing markets. We prove existence and…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
A minimal stochastic dynamical model of the interbank network is introduced, with linear interactions mediated by an integral of recent variations. Defining stress as the variance over the banks' states, the interaction correction to the…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
Understanding and predicting the behavior of large-scale multi-agents in games remains a fundamental challenge in multi-agent systems. This paper examines the role of heterogeneity in equilibrium formation by analyzing how smooth…
The objective of this paper is to identify and analyze the response actions of a set of players embedded in sub-networks in the context of interaction and learning. We characterize strategic network formation as a static game of…
Social storage systems are becoming increasingly popular compared to the existing data backup systems like local, centralized and P2P systems. An endogenously built symmetric social storage model and its aspects like the utility of each…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
Network data has attracted growing interest across scientific domains, prompting the development of various network models. Existing network analysis methods mainly focus on unsigned networks, whereas signed networks, consisting of both…
Strategic interactions between a group of individuals or organisations can be modelled as games played on networks, where a player's payoff depends not only on their actions but also on those of their neighbours. Inferring the network…
We introduce a two-parameter ensemble of random discrete-time Markov models that simultaneously captures critical slowing down and broken detailed balance. Extending a previously studied heterogeneous Markov ensemble, we incorporate…
In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world…
One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been…
We consider a multi-user network where a network manager and selfish users interact. The network manager monitors the behavior of users and intervenes in the interaction among users if necessary, while users make decisions independently to…
We consider a sharing economy network where agents embedded in a graph share their resources. This is a fundamental model that abstracts numerous emerging applications of collaborative consumption systems. The agents generate a random…
In this short note we provide a proof of boundedness of solutions for a network system composed of heterogeneous nonlinear autonomous systems interconnected over a directed graph. The sole assumptions imposed are that the systems are…