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Dynamics of two particles with short range repulsive or attractive interaction is studied numerically in the Harper model. It is shown that interaction leads to appearance of localized states and pure-point spectrum component in the case…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
We numerically examine a bidisperse system of active and passive particles coupled to a resource substrate. The active particles deplete the resource at a fixed rate and move toward regions with higher resources, while all of the particles…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
Quantifying animal interactions is crucial for understanding various ecological processes, including social community structures, predator-prey dynamics, spreading of pathogens and information. Despite the ubiquity of interaction processes…
Most of the published articles on random motions have been devoted to the study of the telegraph process or its generalizations that describe the random motion in $R^n$ of a single particle in a Markov or semi-Markov medium. However, up to…
Recent studies from social, biological, and engineering network systems have drawn attention to the dynamics over signed networks, where each link is associated with a positive/negative sign indicating trustful/mistrustful,…
Two-body scattering of neutral particles in a trap is studied theoretically. The control of the initial state is realized by using optical traps. The collisions inside the trap occur repeatedly; thereby the effect of interaction can be…
The motion of pedestrian crowds (e.g. for simulation of an evacuation situation) can be modeled as a multi-body system of self driven particles with repulsive interaction. We use a few simple situations to determine the simplest allowed…
Activated Random Walk is a system of interacting particles which presents a phase transition and a conjectured phenomenon of self-organized criticality. In this note, we prove that, in dimension 1, in the supercritical case, when a segment…
We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly…
We study a model of multi-excited random walk on a regular tree which generalizes the models of the once excited random walk and the digging random walk introduced by Volkov (2003). We show the existence of a phase transition of the…
In this paper we study subdiffusion in a system with a thin membrane. At the beginning, the random walk of a particle is considered in a system with a discrete time and space variable and then the probability describing the evolution of the…
We study various models of independent particles hopping between energy `traps' with a density of energy barriers $\rho(E)$, on a $d$ dimensional lattice or on a fully connected lattice. If $\rho(E)$ decays exponentially, a true dynamical…
The current article shows how concepts from the areas of random walks, Markov chains, complex networks and image analysis can be naturally combined in order to provide a unified and biologically plausible model relating saliency and visual…
The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…
In this paper we consider a model of spreading information in heterogeneous systems wherein we have two kinds of objects. Some of them are active and others are passive. Active objects can, if they possess information, share it with an…
We consider a random graph model evolving in discrete time-steps that is based on 3-interactions among vertices. Triangles, edges and vertices have different weights; objects with larger weight are more likely to participate in future…