A piecewise deterministic model for a prey-predator community
A piecewise deterministic model for a prey-predator community
复制标题
捕食者群落的分段确定性模型
DOI：
10.1214/16-aap1182
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Manon Costa
中科院分区：
文献类型：
--
作者：
Manon Costa
我们感兴趣的是捕食者种群进化速度比猎物快得多的捕食者群落（例如昆虫-树木群落）。我们引入了一个分段确定性模型，这些食饵-捕食者社区，出现作为一个限制的微观模型时，捕食者的数量趋于无穷大。我们证明了该过程具有唯一不变的概率测度，并且是指数遍历的。进一步，我们重新调整捕食者的动态，以模型捕食者较小的尺寸。这个慢-快系统收敛到一个群落过程，在这个过程中，捕食者的动态平均在捕食者平衡点上。这个平均过程允许一个不变的概率测度，可以显式计算。我们使用数值模拟研究的重标度过程的不变概率测度的收敛性。
We are interested in prey-predator communities where the predator population evolves much faster than the prey's (e.g. insect-tree communities). We introduce a piecewise deterministic model for these prey-predator communities that arises as a limit of a microscopic model when the number of predators goes to infinity. We prove that the process has a unique invariant probability measure and that it is exponentially ergodic. Further on, we rescale the predator dynamics in order to model predators of smaller size. This slow-fast system converges to a community process in which the prey dynamics is averaged on the predator equilibria. This averaged process admits an invariant probability measure which can be computed explicitly. We use numerical simulations to study the convergence of the invariant probability measures of the rescaled processes.
影响因子：
1.8
作者：
Champagnat, Nicolas;Lambert, Amaury
通讯作者：
Lambert, Amaury