Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems

Samuel Cure*, Izaak Neri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
51 Downloads (Pure)

Abstract

We analyse the stability of large, linear dynamical systems of variables that interact through a fully connected random matrix and have inhomogeneous growth rates. We show that in the absence of correlations between the coupling strengths, a system with interactions is always less stable than a system without interactions. Contrarily to the uncorrelated case, interactions that are antagonistic, i.e., characterised by negative correlations, can stabilise linear dynamical systems. In particular, when the strength of the interactions is not too strong, systems with antagonistic interactions are more stable than systems without interactions. These results are obtained with an exact theory for the spectral properties of fully connected random matrices with diagonal disorder.
Original languageEnglish
Article numberA3
Number of pages31
JournalSciPost Physics
Volume14
Issue number5
DOIs
Publication statusPublished - 3 May 2023

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