Systems of random linear equations and the phase transition in MacArthur's resource-competition model
Systems of random linear equations and the phase transition in MacArthur's resource-competition model
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DOI：
10.1209/0295-5075/124/18004
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发表时间：
2018-10-01
期刊：
影响因子：
1.8
通讯作者：
Engel, Andreas
中科院分区：
文献类型：
--
作者：
Landmann, Stefan;Engel, Andreas
复杂的生态系统通常由利用大量不同资源的大量不同物种组成。它们的一些特征不能被只包含少数物种和资源的模型所捕捉。最近，Tikhonov和Monasson已经证明麦克阿瑟资源竞争模型的高维版本显示了一个从“脆弱”到“保护”阶段的阶段转变，在这个阶段，物种集体保护自己免受来自外部的不均匀资源涌入。这里我们指出，这种转变是更普遍的，可以追溯到非负解的存在，随机线性方程组的大系统。利用法卡斯引理，我们将这个问题映射到高维分数体积的性质，我们使用无序系统的统计力学方法来确定分数体积的性质。中国人民解放军版权所有，2018年
Complex ecosystems generally consist of a large number of different species utilizing a large number of different resources. Several of their features cannot be captured by models comprising just a few species and resources. Recently, Tikhonov and Monasson have shown that a high-dimensional version of MacArthur's resource competition model exhibits a phase transition from a "vulnerable" to a "shielded" phase in which the species collectively protect themselves against an inhornogeneous resource influx from the outside. Here we point out that this transition is more general and may be traced back to the existence of non-negative solutions to large systems of random linear equations. Employing Farkas' Lemma we map this problem to the properties of a fractional volume in high dimensions which we determine using methods from the statistical mechanics of disordered systems. Copyright (C) EPLA, 2018