相关论文: Small-world spectra in mean field theory

Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph…

Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…

We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With…

Complex network formalism allows to explain the behavior of systems composed by interacting units. Several prototypical network models have been proposed thus far. The small-world model has been introduced to mimic two important features…

Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these…

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…

We use scaling results to identify the crossover to mean-field behavior of equilibrium statistical mechanics models on a variant of the small world network. The results are generalizable to a wide-range of equilibrium systems. Anomalous…

The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of…

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…

Small world networks interpolate between fully regular and fully random topologies and simultaneously exhibit large local clustering as well as short average path length. Small world topology has therefore been suggested to support network…

One of the hallmarks of real networks is their ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the…

Despite the knowledge that social, economical, and ecological networks are often of a small-world nature with inter-nodal distance growing even slower than logarithmically with system size, we often assume theoretical systems to be outside…

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…

A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, $N$. In this paper, we present a novel derivation of the…

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…

The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…

Dynamical systems driven by strong external signals are ubiquituous in nature and engineering. Here we study "echo state networks", networks of a large number of randomly connected nodes, which represent a simple model of a neural network,…

If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…

We propose a new method to recover global information about a network of interconnected dynamical systems based on observations made at a small number (possibly one) of its nodes. In contrast to classical identification of full graph…