Counting equilibria of large complex systems by instability index
| Autor: | Gérard Ben Arous, Yan V. Fyodorov, Boris A. Khoruzhenko |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Complex systems Multidisciplinary Phase portrait Solenoidal vector field Equilibrium Degrees of freedom (physics and chemistry) Complex system FOS: Physical sciences Mathematical Physics (math-ph) Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Instability Stability (probability) Nonlinear Sciences - Adaptation and Self-Organizing Systems Nonlinear system Physical Sciences Statistical physics Random matrices Stability Adaptation and Self-Organizing Systems (nlin.AO) Random matrix Mathematical Physics |
| Zdroj: | Proc Natl Acad Sci U S A Arous, G B, Fyodorov, Y V & Khoruzhenko, B A 2021, ' Counting equilibria of large complex systems by instability index ', Proceedings of the National Academy of Sciences of the United States of America, vol. 118, no. 34, e2023719118 . https://doi.org/10.1073/pnas.2023719118 |
| ISSN: | 1091-6490 0027-8424 |
| DOI: | 10.1073/pnas.2023719118 |
| Popis: | We consider a nonlinear autonomous system of $N\gg 1$ degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction strength such systems generically undergo an abrupt transition from a trivial phase portrait with a single stable equilibrium into a topologically non-trivial regime of 'absolute instability' where equilibria are on average exponentially abundant, but typically all of them are unstable, unless the dynamics is purely gradient. When interactions increase even further the stable equilibria eventually become on average exponentially abundant unless the interaction is purely solenoidal. We further calculate the mean proportion of equilibria which have a fixed fraction of unstable directions. Comment: Main paper - 7 pages, Supplementary Information - 20 pages. Revised version - minor changes, including adding short discussion of model assumptions |
| Databáze: | OpenAIRE |
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