相关论文: Small-world behavior in a system of mobile element…

We introduce a novel concept of simple loop dwell time and use it to give sufficient conditions for stability of a continuous-time linear switched system where switching between subsystems is governed by an underlying graph. We present a…

Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…

Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the…

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is…

The dynamics of generic stochastic Lotka-Volterra (discrete logistic) systems of the form \cite{Solomon96a} $w_i (t+1) = \lambda(t) w_i (t) + a {\bar w (t)} - b w_i (t) {\bar w(t)}$ is studied by computer simulations. The variables $w_i$,…

We investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one. At each jump, the random walker is subject to a drift that depends on whether it is…

Discoveries of the scale-free and small-world features are reported on a network constructed from the seismic data. It is shown that the connectivity distribution decays as a power law, and the value of the degrees of separation, i.e., the…

Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with…

We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent…

We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…

The small-world property in the context of complex networks implies structural benefits to the processes taking place within a network, such as optimal information transmission and robustness. In this paper, we study a model network of…

Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost…

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…

We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…

We study branching random walks in random i.i.d. environment in $\Z^d, d \geq 1$. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience,…

A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state…

In this work, we have employed Monte Carlo calculations to study the Ising model on a 2D additive small-world network with long-range interactions depending on the geometric distance between interacting sites. The network is initially…

This paper considers a discrete time swarm model of a group of mobile autonomous agents with a simple attraction and repulsion function for swarm aggregation and investigates its stability properties. In particular, it is proved that the…

It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling…

Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect,…