Stability of linear systems on sparse random graphs: the role of sign patterns
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Abstract: Linear stability of dynamical systems is determined by the eigenvalue with the largest real part of Jacobian matrix. For nonsymmetric random graphs, the leading eigenvalue depends strongly on the sign pattern of the weights of the graph. Specifically, for random graphs with sign-antisymmetric weights, the leading eigenvalue is finite in the infinite size limit, while if there is a finite fraction of sign-symmetric weights, then the leading eigenvalue diverges as a function of system size. This result demonstrates the strong stabilising nature of sign-antisymmetric weights. In this seminar, I will first present numerical results on the influence of the sign pattern on the leading eigenvalue, followed by theoretical results explaining these numerical experiments. |
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[1] A M Mambuca, C Cammarota, and I Neri, Physical Review E (2022) |
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[2] P Valigi, I Neri, and C Cammarota, Journal of Physics: Complexity (2024) |
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[3] P Valigi, J Baron, et al., arXiv 2507.20225 (2025). |