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Persistence in Stochastic Lotka--Volterra food chains with intraspecific competition. (arXiv:1704.07501v1 [math.PR])
来源于:arXiv
This paper is devoted to the analysis of a simple Lotka-Volterra food chain
evolving in a stochastic environment. It can be seen as the companion paper of
Hening and Nguyen `17 where we have characterized the persistence and
extinction of such a food chain under the assumption that there is no
intraspecific competition among predators. In the current paper we focus on the
case when all the species experience intracompetition. The food chain we
analyze consists of one prey and $n-1$ predators. The $j$th predator eats the
$j-1$th species and is eaten by the $j+1$th predator; this way each species
only interacts with at most two other species - the ones that are immediately
above or below it in the trophic chain. We show that one can classify, based on
the invasion rates of the predators (which we can determine from the
interaction coefficients of the system via an algorithm), which species go
extinct and which converge to their unique invariant probability measure. We
obtain stronger res 查看全文>>