Related papers: Synchronous vs. asynchronous dynamics of diffusion…
Using Monte Carlo simulations we have studied the transition from an "active" steady state to an absorbing "inactive" state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the…
Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two…
We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with asymmetric rates (the sum of which is one) to the right or left…
We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…
In a recent article [1] we surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in…
We investigate the spatiotemporal dynamics of coupled circle map lattices, evolving under synchronous (parallel) updating on one hand and asynchronous (random) updating rules on the other. Synchronous evolution of extended spatiotemporal…
Diffusion-limited reaction A+A->inert with anisotropic hopping on the d=1 lattice, is solved exactly for a simultaneous updating, discrete time-step dynamics. Diffusion-dominated processes slow down as the anisotropy increases. For large…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via…
This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random dynamical system is formulated in a two-step procedure, at…
Asynchronous event sequences are the basis of many applications throughout different industries. In this work, we tackle the task of predicting the next event (given a history), and how this prediction changes with the passage of time.…
We investigate the dynamics of an array of logistic maps coupled with random delay times. We report that for adequate coupling strength the array is able to synchronize, in spite of the random delays. Specifically, we find that the…
We use a boolean cellular automaton model to describe the diffusion limited dynamics of the irreversible reaction A+A->A+S on a 1D lattice. We derive a set of equations for the dynamics of the empty interval probabilities from which…
In Part II [3] we carried out a detailed mean-square-error analysis of the performance of asynchronous adaptation and learning over networks under a fairly general model for asynchronous events including random topologies, random link…
Coupled map lattices are paradigmatic models of many collective phenomena. However, quite different patterns can emerge depending on the updating scheme. While in early versions, maps were updated synchronously, there has been in recent…
Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal…
Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of…
Two types of synchronization, Achronal Synchronization and Isochronous synchronization are investigated numerically when unidirectionally coupled laser systems are considered both on fast and slow dynamics by studying the correlation…
We study the synchronous dynamics of the Hopfield model when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. We use a generating functional technique to derive analytical expressions for the order parameters…
A systematic theory for the diffusion--limited reaction processes $A + A \to 0$ and $A \to (m+1) A$ is developed. Fluctuations are taken into account via the field--theoretic dynamical renormalization group. For $m$ even the mean field rate…