Related papers: Small-world behavior in a system of mobile element…
We consider continuous time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter a, which is set…
We investigate the dynamic phase transition from partially or fully arrested state to spatiotemporal chaos in coupled logistic maps on a small-world network. Persistence of local variables in coarse grained sense acts as an excellent order…
We report numerical evidence that an epidemic-like model, which can be interpreted as the propagation of a rumor, exhibits critical behavior at a finite randomness of the underlying small-world network. The transition occurs between a…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
The dynamical discrete web (DDW), introduced in recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical parameter s. The evolution is by…
The aim of the study was to compare the epidemic spread on static and dynamic small-world networks. The network was constructed as a 2-dimensional Watts-Strogatz model (500x500 square lattice with additional shortcuts), and the dynamics…
We study networks representing the dynamics of elementary 1-d cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node…
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…
Small world models are networks consisting of many local links and fewer long range `shortcuts'. In this paper, we consider some particular instances, and rigorously investigate the distribution of their inter--point network distances. Our…
During epidemics, the population is asked to Socially Distance, with pairs of individuals keeping two meters apart. We model this as a new optimization problem by considering a team of agents placed on the nodes of a network. Their common…
We introduce a self-organized model of graph evolution associated with preferential network random walkers. The idea is developed by using two different types of walkers, the interactions of which lead to a dynamic graph. The walkers of the…
We consider systems that are well modelled as a networks that evolve in time, which we call {\it Moving Neighborhood Networks}. These models are relevant in studying cooperative behavior of swarms and other phenomena where emergent…
In this paper we analyze the effect of a non-trivial topology on the dynamics of the so-called Naming Game, a recently introduced model which addresses the issue of how shared conventions emerge spontaneously in a population of agents. We…
We study the mixing time of random walks on small-world networks modelled as follows: starting with the 2-dimensional periodic grid, each pair of vertices $\{u,v\}$ with distance $d>1$ is added as a "long-range" edge with probability…
Researchers have long observed that the ``small-world" property, which combines the concepts of high transitivity or clustering with a low average path length, is ubiquitous for networks obtained from a variety of disciplines, including…
This paper proposes the problem of modeling video sequences of dynamic swarms (DS). We define DS as a large layout of stochastically repetitive spatial configurations of dynamic objects (swarm elements) whose motions exhibit local…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance,…
We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…
We study excitation waves on a Newman-Watts small-world network model of coupled excitable elements. Depending on the global coupling strength, we find differing resilience to the added long-range links and different mechanisms of…