Related papers: Dynamic rewiring in small world networks

We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model by a low-dimensional system of equations permitting analytical…

Continuing in the steps of Jon Kleinberg's and others celebrated work on decentralized search in small-world networks, we conduct an experimental analysis of a dynamic algorithm that produces small-world networks. We find that the algorithm…

Disease awareness in infection dynamics can be modeled with adaptive contact networks whose rewiring rules reflect the attempt by susceptibles to avoid infectious contacts. Simulations of this type of models show an active phase with…

A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…

We study the dynamics of an epidemic-like model for the spread of a rumor on a small-world network. It has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network…

We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be…

Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…

In this paper, we offer a competing dynamic analysis of the one-dimensional Ising model built on the small-world network (SWN). Adding-type SWNs are investigated in detail using a simplified Hamiltonian of mean-field nature, and the result…

We study the thermodynamic properties of spin systems on small-world hypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin interactions onto a one-dimensional Ising chain with nearest-neighbor interactions. We use…

We study the dynamical behaviour of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties…

Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories…

In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…

Many real world networks are characterized by adaptive changes in their topology depending on the dynamic state of their nodes. Here we study epidemic dynamics in an adaptive network, where susceptibles are able to avoid contact with…

Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…

We calculate equilibrium solutions for Ising spin models on `small world' lattices, which are constructed by super-imposing random and sparse Poissonian graphs with finite average connectivity c onto a one-dimensional ring. The nearest…

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems.…

The zero-temperature Glauber dynamics of the ferromagnetic Ising model on small-world networks, rewired from a two-dimensional square lattice, has been studied by numerical simulations. For increasing disorder in finite networks, the…

Small-world networks, which combine randomized and structured elements, are seen as prevalent in nature. Several random graph models have been given for small-world networks, with one of the most fruitful, introduced by Jon Kleinberg,…

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…