Related papers: Small-World Network Effect in Competing Glauber- a…
Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the…
On directed Barabasi-Albert networks with two and seven neighbours selected by each added site, the Ising model does not seem to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation follows an…
The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics…
Societies are quintessential open systems, shaped by internal dynamics as well as external influences. The question is how these external influences alter the collective behavior and network dynamics. To answer this, we investigate…
Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random…
We introduce and define three types of small worlds: small worlds based on the diameter of the network (SWD), those based on the average geodesic distance between nodes (SWA), and those based on the median geodesic distance (SWMd). These…
In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the…
We analyse the equilibrium behaviour and non-equilibrium dynamics of sparse Boolean networks with self-interactions that evolve according to synchronous Glauber dynamics. Equilibrium analysis is achieved via a novel application of the…
An Ising model with local Glauber dynamics is studied under the influence of additional kinetic restrictions for the spin-flip rates depending on the orientation of neighboring spins. Even when the static interaction between the spins is…
In statistical network analysis it is common to observe so called interaction data. Such data is characterized by actors forming the vertices and interacting along edges of the network, where edges are randomly formed and dissolved over the…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…
Interactions in biology and social systems are not restricted to pairwise but can take arbitrary sizes. Extensive studies have revealed that the arbitrary-sized interactions significantly affect the spreading dynamics on networked systems.…
A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in $\mathbb R^d$ which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure $\mu$…
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 investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for…
We study the effect of competition between short-term synaptic depression and facilitation on the dynamical properties of attractor neural networks, using Monte Carlo simulation and a mean field analysis. Depending on the balance between…
The dynamics of two 1/2-spin qubits under the influence of a quantum Heisenberg XY type spin-bath is studied. After the Holstein-Primakoff transformation, a novel numerical polynomial scheme is used to give the time-evolution calculation of…
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…
We consider a one-dimensional Ising model each of whose $N$ spins is in contact with two thermostats of distinct temperatures $T_1$ and $T_2$. Under Glauber dynamics the stationary state happens to coincide with the equilibrium state at an…