相关论文: Path-integral approach to the dynamics in sparse r…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
The theory of large random matrices has proved an invaluable tool for the study of systems with disordered interactions in many quite disparate research areas. Widely applicable results, such as the celebrated elliptic law for dense random…
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
We propose a Kuramoto model of coupled oscillators on a time-varying graph, whose dynamics is dictated by a Markov process in the space of graphs. The simplest representative is considering a base graph and then the subgraph determined by…
In this paper, we study convergence of coupled dynamical systems on convergent sequences of graphs to a continuum limit. We show that the solutions of the initial value problem for the dynamical system on a convergent graph sequence tend to…
We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours…
In this work we study of the dynamics of large size random neural networks. Different methods have been developed to analyse their behavior, most of them rely on heuristic methods based on Gaussian assumptions regarding the fluctuations in…
Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the modeling procedure. On one hand, this can offer a more…
We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…
The Kuramoto model (KM) of coupled phase oscillators on scale free graphs is analyzed in this work. The W-random graph model is used to define a convergent family of sparse graphs with power law degree distribution. For the KM on this…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
The Kuramoto model is one of the most widely studied model for describing synchronization behaviors in a network of coupled oscillators, and it has found a wide range of applications. Finding all possible frequency synchronization…
We consider systems of mean-field interacting diffusions, where the pairwise interaction structure is described by a sparse (and potentially inhomogeneous) random graph. Examples include the stochastic Kuramoto model with pairwise…
Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
This paper considers some designs for sampling and interventions in dynamic networks and spatial temporal settings. The sample spreads through the population largely by tracing network links, although random sampling or spatial designs may…
We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…
In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…
This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…
The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a…