Random Antagonistic Matrices

Abstract

The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries ${\mathcal{A}}_{i,j}$ and ${\mathcal{A}}_{j,i}$ are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology.

14 pages, 6 figures. References and text updated

References in corpus (3)

• Nonlinear Analogue of the May-Wigner Instability Transition
• Conditional Random Matrix Ensembles and the Stability of Dynamical Systems
• Level spacings for weakly asymmetric real random matrices and application to two-color QCD with chemical potential

Cited by in corpus (2)

• Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations
• Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems