Related papers: Dynamics of Nonlinear Random Walks on Complex Netw…
We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Open quantum walks often lead to a classical asymptotic behavior. Here, we look for a simple open quantum walk whose asymptotic behavior can be non-classical. We consider a discrete-time quantum walk on n-cycle subject to a random…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination…
In this work, we study the dynamical robustness in a system consisting of both active and inactive oscillators. We analytically show that the dynamical robustness of such system is determined by the cross link density between active and…
This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
This work addresses synchronization in transient, non-linear stochastic dynamics corresponding to accesses performed by self-avoiding walks originating at each node of a complex network. More specifically, the synchronizability of accesses…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…
In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…
We introduce a strategy of navigation in undirected networks, including regular, random, and complex networks, that is inspired by L\'evy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
For Markov chains with a partially ordered finite state space we show strong stationary duality under the condition of M\"obius monotonicity of the chain. We show relations of M\"obius monotonicity to other definitions of monotone chains.…