Related papers: Coexistence in discrete time Multi-type competing …
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
We consider the continuous-time frog model on $\mathbb{Z}$. At time $t = 0$, there are $\eta (x)$ particles at $x\in \mathbb{Z}$, each of which is represented by a random variable. In particular, $(\eta(x))_{x \in \mathbb{Z} }$ is a…
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…
In the two-type Richardson model on a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, each vertex is at a given time in state $0$, $1$ or $2$. A $0$ flips to a $1$ (resp.\ $2$) at rate $\lambda_1$ ($\lambda_2$) times the number of…
Coexistence of competing species is, due to unavoidable fluctuations, always transient. In this Letter, we investigate the ultimate survival probabilities characterizing different species in cyclic competition. We show that they often obey…
We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with…
We study the frog model with death on the biregular tree $\mathbb{T}_{d_1,d_2}$. Initially, there is a random number of awake and sleeping particles located on the vertices of the tree. Each awake particle moves as a discrete-time…
Local coexistence of species in large ecosystems is traditionally explained within the broad framework of niche theory. However, its rationale hardly justifies rich biodiversity observed in nearly homogeneous environments. Here we consider…
A binary mixture of two-different-sizes proliferating motile disks is studied. As growth is space-limited, we focus on the conditions such that there is coexistence of both large and small disks, or dominance of the larger disks. The study…
We study a class of interacting particle systems on $\mathbb{R}$ with two types. Particles evolve by independent jumps sampled from a fixed distribution, with type-dependent jump rates $v_+$, $v_-$ and stochastic type switching driven by…
Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…
A biologically motivated model for spatio-temporal coexistence of two competing species is studied by mean-field theory and numerical simulations. In d>1 dimensions the phase diagram displays an extended region where both species coexist,…
We study a discrete time spatial branching system on $\mathbb{Z}^d$ with logistic-type local regulation at each deme depending on a weighted average of the population in neighboring demes. We show that the system survives for all time with…
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…
There are two types of particles interacting on a homogeneous tree of degree d + 1. The particles of the first type colonize the empty space with exponential rate 1, but cannot take over the vertices that are occupied by the second type.…
Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The…
A class of variational models describing ecological systems of k species competing for the same resources is investigated. The occurrence of coexistence in minimal energy solutions is discussed and positive results are proven for suitably…
The aim of this work is to demonstrate that the continuous-time frog model can spread arbitrary fast. The set of sites visited by an active particle can become infinite in a finite time.
The frog model is an interacting particle system on a graph. Active particles perform independent simple random walks, while sleeping particles remain inert until visited by an active particle. Some number of sleeping particles are placed…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…