论文标题
退化的随机lotka-volterra食物链中的随机持久性
Stochastic persistence in degenerate stochastic Lotka-Volterra food chains
论文作者
论文摘要
我们认为在随机微分方程代表的随机环境中可能具有特异性竞争的Lotka-Volterra食物链模型。在非分类环境中，A. Hening和D. Nguyen已经研究了该模型。他们提供了随机持久性和灭绝的条件。在本文中，我们将其结果扩展到堕落的情况，在这种情况下，顶部或底部物种会受到随机扰动的影响。在持久条件下，存在一个独特的不变概率度量，该概率度量由$ \ mathbb {r} _+^n $具有光滑密度的内部支持。 此外，我们研究了一个更通用的模型，在该模型中，我们提供了新的条件，使得表征半组以指数率或多项式为单位的差异概率度量的收敛。这将用于随机Lotka-Volterra食物链，以查看如果所有物种都会发生特异性竞争，则收敛速率是指数呈指数呈指数的，而在其他情况下则是多项式。
We consider a Lotka-Volterra food chain model with possibly intra-specific competition in a stochastic environment represented by stochastic differential equations. In the non-degenerate setting, this model has already been studied by A. Hening and D. Nguyen. They provided conditions for stochastic persistence and extinction. In this paper, we extend their results to the degenerate situation in which the top or the bottom species is subject to random perturbations. Under the persistence condition, there exists a unique invariant probability measure supported by the interior of $\mathbb{R}_+^n$ having a smooth density. Moreover, we study a more general model, in which we give new conditions which make it possible to characterise the convergence of the semi-group towards the unique invariant probability measure either at an exponential rate or at a polynomial one. This will be used in the stochastic Lotka-Volterra food chain to see that if intra-specific competition occurs for all species, the rate of convergence is exponential while in the other cases it is polynomial.
