Related papers: Dynamics of Nonlinear Random Walks on Complex Netw…

Random walks on discrete lattices are fundamental models that form the basis for our understanding of transport and diffusion processes. For a single random walker on complex networks, many properties such as the mean first passage time and…

Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…

To study a chaotic itinerant motion among varieties of ordered states, we propose a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line, and a Markov chain with a transition…

Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently…

When a fluid comprised of multiple phases or constituents flows through a network, non-linear phenomena such as multiple stable equilibrium states and spontaneous oscillations can occur. Such behavior has been observed or predicted in a…

Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…

A system is called antifragile when damage acts as a constructive element improving the performance of a global function. In this paper, we analyze the emergence of antifragility in the movement of random walkers on networks with modular…

Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…

In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…

What can one say on convergence to stationarity of a finite state Markov chain that behaves "locally" like a nearest neighbor random walk on ${\mathbb Z}$ ? The model we consider is a version of nearest neighbor lazy random walk on the…

We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical…

The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes one we developed previously (Phys. Rev. E v.79, 011110, 2009) in order to describe the Levy type stochastic processes in terms of continuous…

We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…

Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…

One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles…

We find that a symbolic walk (performed by a walker with memory given by a Bernoulli shift) is able to distinguish between the random or chaotic topology of a given network. We show this result by means of studying the undirected baker…

We introduce a family of quantum walks on cycles parametrized by their liveliness, defined by the ability to execute a long-range move. We investigate the behaviour of the probability distribution and time-averaged probability distribution.…

We address the dynamics of continuous-time quantum walks on one-dimensional disordered lattices inducing dynamical noise in the system. Noise is described as time-dependent fluctuations of the tunneling amplitudes between adjacent sites,…