Related papers: The Symbiotic Contact Process
Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…
The phase transition of the one-dimensional, diffusive pair contact process (PCPD) is investigated by N cluster mean-field approximations and high precision simulations. The N=3,4 cluster approximations exhibit smooth transition line to…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of…
We consider a generalization of the contact process stochastic model, including an additional autocatalitic process. The phase diagram of this model in the proper two-parameter space displays a line of transitions between an active and an…
Statistical physics can describe the behavior of microbial populations consisting of many heterogeneous individuals. A direct consequence is the existence of phase transitions, where the behavior of a population changes discontinuously upon…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The…
We study a model that generalizes the CP with diffusion. An additional transition is included in the model so that at a particular point of its phase diagram a crossover from the directed percolation to the compact directed percolation…
We study degree-penalized contact processes on Galton-Watson trees (GW) and the configuration model. The model we consider is a modification of the usual contact process on a graph. In particular, each vertex can be either infected or…
We study the discrete-time threshold-$\theta \geq 2$ contact process on random graphs of general degrees. For random graphs with a given degree distribution $\mu$, we show that if $\mu$ is lower bounded by $\theta+2$ and has finite $k$th…
We study the independent alignment percolation model on $\mathbb{Z}^d$ introduced by Beaton, Grimmett and Holmes [arXiv:1908.07203]. It is a model for random intersecting line segments defined as follows. First the sites of $\mathbb{Z}^d$…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
Consider subcritical Bernoulli bond percolation with fixed parameter p<p_c. We define a dependent site percolation model by the following procedure: for each bond cluster, we colour all vertices in the cluster black with probability r and…
We consider a general class of contact processes on $\mathbb{Z}^d$ with potentially long-range interactions. By adapting well established renormalization arguments to the long-range setting we extend by now classical results for…
In this article, we present two novel variants of the contact process. In the first variant individuals carry a viral load. An individual with viral load zero is classified as healthy and otherwise infected. If an individual becomes…
Recent progress in the study of the contact process [2] has verified that the extinction-survival threshold $\lambda_1$ on a Galton-Watson tree is strictly positive if and only if the offspring distribution $\xi$ has an exponential tail. In…
We consider directed percolation processes for particle types A and B coupled unidirectionally by a transmutation reaction A -> B. It is shown that the strong coupling regime of this recently introduced problem defines a universality class…
Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two…
In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of…