Related papers: Phase Transition for the Chase-Escape Model on 2D …
This paper provides a survey of known results and open problems for the two-type Richardson model, which is a stochastic model for competition on $\mathbb{Z}^d$. In its simplest formulation, the Richardson model describes the evolution of a…
In this study, we investigate the dynamics of a spatial and non spatial prey-predator interaction model that includes the following: (i) fear effect incorporated in prey birth rate; (ii) group defence of prey against predators; and (iii)…
We study a stochastic predator-prey model on a square lattice, where each of the six species has two superior and two inferior partners. The invasion probabilities between species depend on the predator-prey pair and are supplemented by…
Pairwise particle-exchange model on a linear lattice is solved exactly by a new rate-equation method. Lattice sites are occupied by particles A and B which can exchange irreversibly provided the local energy in reduced. Thus, the model…
The first arrivals among $N$ Brownian particles is ubiquitous in the life sciences, as it often trigger cellular processes from the molecular level. We study here the case where stochastic particles, which represent molecules, proteins or…
A competition process on $\mathbb{Z}^d$ is considered, where two species compete to color the sites. The entities are driven by branching random walks. Specifically red (blue) particles reproduce in discrete time and place offspring…
We prove that chase-escape with conversion on the complete graph undergoes a phase transition at equal fitness and derive simple asymptotic formulas for the extinction probability, the total number of converted sites, and the expected…
This paper presents a system of stochastic differential equations (SDEs) as mathematical model to describe the spatial-temporal dynamics of predator-prey system in an artificial aquatic environment with schooling behavior imposed upon the…
We investigate a model of a parasite population invading spatially distributed immobile hosts on a graph, which is a modification of the frog model. Each host has an unbreakable immunity against infection with a certain probability $1-p$…
We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system…
The role of predator evasion mediated by chemical signaling is studied in a diffusive prey-predator model when prey-taxis is taken into account (model A) or not (model B) with taxis strength coefficients $\chi$ and $\xi$ respectively. In…
A one-dimensional driven lattice gas with disorder in the particle hopping probabilities is considered. It has previously been shown that in the version of the model with random sequential updating, a phase transition occurs from a low…
We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction…
We study models of spatial growth processes where initially there are sources of growth (indicated by the colour green) and sources of a growth-stopping (paralyzing) substance (indicated by red). The green sources expand and may merge with…
Recent exact results for a particle-exchange model on a linear lattice, with only irreversible moves reducing the local energy allowed, are reviewed. This model describes a zero-temperature Kawasaki-type phase separation process which…
We study equilibrium properties of binary lattice-gases comprising $A$ and $B$ particles, which undergo continuous exchanges with their respective reservoirs, maintained at chemical potentials $\mu_A = \mu_B = \mu$. The particles interact…
We consider the Bose-Hubbard model with particle losses at one lattice site. For the non-interacting case, we find that half of the bosons of an initially homogeneous particle distribution, are not affected by dissipation that only acts on…
In this paper we study threshold-one contact processes on lattices and regular trees. The asymptotic behavior of the critical infection rates as the degrees of the graphs growing to infinity are obtained. Defining \lambda_c as the supremum…
We study a variant of the cyclic Lotka-Volterra model with three-agent interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors game, the model describes an ideal ecosystem in which cyclic competition among three species…
Molecular kinetic simulations are typically used to accurately describe the tenuous regions of the upper atmospheres on planetary bodies. These simulations track the motion of particles representing real atmospheric atoms and/or molecules…