随机切换的Lotka-Volterra食物链的持久性

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
A. Bourquin
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引用次数: 3

摘要

我们考虑一个由$N$Lotka-Volterra食物链之间的随机切换得到的动力系统。我们的关键假设是,至少有两个矢量场只在分配给第一个物种的增长率的资源上有所不同。我们将证明平均向量场的正平衡的存在等价于所有物种的持续存在。在此条件下,半群在正正交上以指数速度收敛到唯一不变的概率测度。如果这个条件不成立,我们有两种可能。第一种可能性是灭绝情况,即一组物种以指数速度灭绝,而剩余物种的分布则弱地收敛于另一种不变的概率度量。第二种可能性是临界情况,在这种情况下,一些物种的持久性较弱,而剩下的一些物种则以指数级的速度灭绝。我们还将分析该模型对参数的敏感性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Persistence in randomly switched Lotka-Volterra food chains
We consider a dynamical system obtained by the random switching between $N$Lotka-Volterra food chains. Our key assumption will be that at least two vector fields only differ on the resources allocated to the growth rate of the first species. We will show that the existence of a positive equilibrium of the average vector field is equivalent to the persistence of all species. Under this condition, the semi-group converges exponentially quickly to a unique invariant probability measure on the positive orthant. If this condition fails to hold, we have two possibilities. The first possibility is the extinction case, in which a group of species becomes extinct exponentially quicklywhile the distribution of the remaining species converges weakly to another invariant probability measure. The second possibility is the critical case, in which there is a weaker form of persistence of some species, whilst some of the remaining become extinct exponentially quickly. We will also analyse the sensitivity of this model to the parameters.
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来源期刊
Esaim-Probability and Statistics
Esaim-Probability and Statistics STATISTICS & PROBABILITY-
CiteScore
1.00
自引率
0.00%
发文量
14
审稿时长
>12 weeks
期刊介绍: The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.
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