Landmann , Stefan and Engel, Andreas (2018) Systems of random linear equations and the phase transition in MacArthur's resource-competition model. epl, 124 (1). ISSN 1286-4854

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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 inhomogeneous 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.

Item Type: Article
Subjects: Science and mathematics > Physics
Divisions: Faculty of Mathematics and Science > Institute of Physics (IfP)
Date Deposited: 31 Jan 2019 11:58
Last Modified: 31 Jan 2019 11:58
URN: urn:nbn:de:gbv:715-oops-39411

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