论文标题
空间随机逻辑模型中的灭绝阈值：空间均匀情况
Extinction threshold in spatial stochastic logistic model: Space homogeneous case
论文作者
论文摘要
我们使用一阶扰动在平均场方程以外的一阶扰动。在均匀的空间情况下（即，当密度是非空间的并且协方差是不变的）时，我们表明扰动会随着时间而趋向于无穷大；这产生了固定密度的一阶近似。接下来，我们研究关键死亡率---最小的恒定死亡率，确保人口灭绝 - - 作为平均场缩放参数$ \ varepsilon> 0 $的函数。我们发现关键死亡率的渐近扩展（$ \ varepsilon \ to0 $）的领先术语显然有所不同。
We consider the extinction regime in the spatial stochastic logistic model in $\mathbb{R}^d$ (a.k.a. Bolker--Pacala--Dieckmann--Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space homogeneous case (i.e. when the density is non-spatial and the covariance is translation invariant), we show that the perturbation converges as time tends to infinity; that yields the first-order approximation for the stationary density. Next, we study the critical mortality---the smallest constant death rate which ensures the extinction of the population---as a function of the mean-field scaling parameter $\varepsilon>0$. We find the leading term of the asymptotic expansion (as $\varepsilon\to0$) of the critical mortality which is apparently different for the cases $d\geq3$, $d=2$, and $d=1$.
