竞争接触过程共存的一个新结果

多类型接触过程的生存与共存

Survival and coexistence for a multitype contact process

研究了$d$维整数格和正则树上具有等死亡率和不等出生率的多型接触过程的遍历论。我们证明了，在一定的时间间隔内的出生率有共存的树，这是由Neuhauser的结果是不可能的格。我们还证明了一个全收敛的结果时，较大的出生率落在这个区间之外。

Coexistence in competing first passage percolation with conversion

We introduce a two-type first passage percolation competition model on infinite connected graphs as follows. Type 1 spreads through the edges of the graph at rate 1 from a single distinguished site, while all other sites are initially vacant. Once a site is occupied by type 1, it converts to type 2 at rate $ρ>0$. Sites occupied by type 2 then spread at rate $λ>0$ through vacant sites \emph{and} sites occupied by type 1, whereas type 1 can only spread through vacant sites. If the set of sites occupied by type 1 is non-empty at all times, we say type 1 \emph{survives}. In the case of a regular $…

局部调节竞争种群的共存与分支湮灭随机游动的生存

Coexistence in locally regulated competing populations and survival of branching annihilating random walk

我们提出了两个模型的一对竞争种群的进化。两者都是基于网格的。第一个是完全空间模型之间的妥协，这似乎不服从分析结果，和相互作用的粒子系统模型，不，目前，将所有的竞争策略，人口可能采取。第二种方法是第一种方法的简化，即竞争只发生在格点内，每个格点内的总总体规模为常数。在特殊情况下，第二个模型是一个分支零化随机游动的对偶。对于每个模型，使用定向渗流的比较，我们表明，对于某些参数值，两个人口将共存的所有时间与正概率。作为推论，我们推导出的所有时间的分支零化随机游动足够大的分支率的生存。我们还提出了一些与空间在两个种群的生存概率中的作用有关的图表。

一类带季节的多类型接触过程的共存性

Coexistence for a multitype contact process with seasons

我们引入了一个多类型的接触过程的时间异质性，涉及两个物种竞争空间上的$d$维整数格。时间分为季节，交替称为季节1和季节2。我们证明，有一个开集的参数，这两个物种可以共存时，他们的扩散范围是足够大的。数值模拟还表明，三个物种可以共存的两个季节的存在。这与时间齐次多型接触过程的长期行为形成对比，在时间齐次多型接触过程中，当死亡率相等时，具有较高出生率的物种胜过其他物种。

Non-equilibrium multi-scale analysis and coexistence in competing first passage percolation

The main contribution of this paper is the development of a novel approach to multi-scale analysis that we believe can be used to analyse processes with non-equilibrium dynamics. Our approach will be referred to as \emph{multi-scale analysis with non-equilibrium feedback} and will be used to analyse a natural random growth process with competition on $\mathbb{Z}^d$ called \emph{first passage percolation in a hostile environment} that consists of two first passage percolation processes $FPP_1$ and $FPP_λ$ that compete for the occupancy of sites. Initially, $FPP_1$ occupies the origin and spread…

Coexistence of competing first passage percolation on hyperbolic graphs

We study a natural growth process with competition, which was recently introduced to analyze MDLA, a challenging model for the growth of an aggregate by diffusing particles. The growth process consists of two first-passage percolation processes $\text{FPP}_1$ and $\text{FPP}_λ$, spreading with rates $1$ and $λ>0$ respectively, on a graph $G$. $\text{FPP}_1$ starts from a single vertex at the origin $o$, while the initial configuration of $\text{FPP}_λ$ consists of infinitely many \emph{seeds} distributed according to a product of Bernoulli measures of parameter $μ>0$ on $V(G)\setminus \{o\}$. …

The competitive exclusion principle in stochastic environments

In its simplest form, the competitive exclusion principle states that a number of species competing for a smaller number of resources cannot coexist. However, it has been observed empirically that in some settings it is possible to have coexistence. One example is Hutchinson's `paradox of the plankton'. This is an instance where a large number of phytoplankton species coexist while competing for a very limited number of resources. Both experimental and theoretical studies have shown that temporal fluctuations of the environment can facilitate coexistence for competing species. Hutchinson conje…