Volume 124, Number 1, October 2018
|Number of page(s)||5|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||05 November 2018|
Systems of random linear equations and the phase transition in MacArthur's resource-competition model
Carl von Ossietzky Universität, Institut für Physik - D-26111 Oldenburg, Germany
Received: 29 June 2018
Accepted: 10 October 2018
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.
PACS: 87.23.Cc – Population dynamics and ecological pattern formation / 05.70.Fh – Phase transitions: general studies / 02.10.Ud – Linear algebra
© EPLA, 2018
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