# Random antagonistic matrices

@article{Cicuta2016RandomAM, title={Random antagonistic matrices}, author={Giovanni M Cicuta and Luca Guido Molinari}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2016}, volume={49} }

The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries i , j and 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.

## 2 Citations

### Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems

- Mathematics
- 2021

We analyse the stability of large, linear dynamical systems of variables that in-teract through a fully connected random matrix and have inhomogeneous growth rates. We show that in the absence of…

### Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations.

- MathematicsPhysical review. E
- 2022

An exact theory is developed for the spectral distribution and the leading eigenvalue of the corresponding sparse Jacobian matrices of large dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions that reveals that the nature of local interactions have a strong influence on system's stability.

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