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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2112.13498 |
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| _version_ | 1866918263587340288 |
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| author | Cure, Samuel Neri, Izaak |
| author_facet | Cure, Samuel Neri, Izaak |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_13498 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems Cure, Samuel Neri, Izaak Disordered Systems and Neural Networks 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. |
| title | Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2112.13498 |