Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems
We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the behaviour of the leading eigenvalue in different type of ran...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | Journal of Physics: Complexity |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-072X/ad2698 |
| _version_ | 1797271825161388032 |
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| author | Pietro Valigi Izaak Neri Chiara Cammarota |
| author_facet | Pietro Valigi Izaak Neri Chiara Cammarota |
| author_sort | Pietro Valigi |
| collection | DOAJ |
| description | We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the behaviour of the leading eigenvalue in different type of random matrices (including interaction matrices and Jacobian-like matrices), relevant for the assessment of different types of dynamical stability. By comparing numerical results on Erdős–Rényi and Husimi graphs with sign-antisymmetric interactions or mixed sign patterns, we propose a sufficient criterion, called strong local sign stability , for stability not to be affected by system size, as traditionally implied by the complexity-stability trade-off in conventional models of random matrices. The criterion requires sign-antisymmetric or unidirectional interactions and a local structure of the graph such that the number of cycles of finite length do not increase with the system size. Note that the last requirement is stronger than the classical local tree-like condition, which we associate to the less stringent definition of local sign stability , also defined in the paper. In addition, for strong local sign stable graphs which show stability to linear perturbations irrespectively of system size, we observe that the leading eigenvalue can undergo a transition from being real to acquiring a nonnull imaginary part, which implies a dynamical transition from nonoscillatory to oscillatory linear response to perturbations. Lastly, we ascertain the discontinuous nature of this transition. |
| first_indexed | 2024-03-07T14:15:47Z |
| format | Article |
| id | doaj.art-9c2b91be06694ccb9e0b48fcbd32ee87 |
| institution | Directory Open Access Journal |
| issn | 2632-072X |
| language | English |
| last_indexed | 2024-03-07T14:15:47Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Journal of Physics: Complexity |
| spelling | doaj.art-9c2b91be06694ccb9e0b48fcbd32ee872024-03-06T12:30:03ZengIOP PublishingJournal of Physics: Complexity2632-072X2024-01-015101501710.1088/2632-072X/ad2698Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystemsPietro Valigi0https://orcid.org/0009-0007-1593-1325Izaak Neri1https://orcid.org/0000-0001-9529-5742Chiara Cammarota2https://orcid.org/0000-0003-3443-6905Department of Physics, Sapienza University of Rome , P.le Aldo Moro 5, Rome 00185, ItalyDepartment of Mathematics, King’s College London , Strand, London WC2R 2LS, United KingdomDepartment of Physics, Sapienza University of Rome , P.le Aldo Moro 5, Rome 00185, Italy; INFN: Istituto Nazionale di Fisica Nucleare, Sezione di Roma I , P.le Aldo Moro 5, Rome 00185, ItalyWe study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the behaviour of the leading eigenvalue in different type of random matrices (including interaction matrices and Jacobian-like matrices), relevant for the assessment of different types of dynamical stability. By comparing numerical results on Erdős–Rényi and Husimi graphs with sign-antisymmetric interactions or mixed sign patterns, we propose a sufficient criterion, called strong local sign stability , for stability not to be affected by system size, as traditionally implied by the complexity-stability trade-off in conventional models of random matrices. The criterion requires sign-antisymmetric or unidirectional interactions and a local structure of the graph such that the number of cycles of finite length do not increase with the system size. Note that the last requirement is stronger than the classical local tree-like condition, which we associate to the less stringent definition of local sign stability , also defined in the paper. In addition, for strong local sign stable graphs which show stability to linear perturbations irrespectively of system size, we observe that the leading eigenvalue can undergo a transition from being real to acquiring a nonnull imaginary part, which implies a dynamical transition from nonoscillatory to oscillatory linear response to perturbations. Lastly, we ascertain the discontinuous nature of this transition.https://doi.org/10.1088/2632-072X/ad2698random matricessparse random graphscomplex dynamical systemslinear stabilitysparse ecosystems |
| spellingShingle | Pietro Valigi Izaak Neri Chiara Cammarota Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems Journal of Physics: Complexity random matrices sparse random graphs complex dynamical systems linear stability sparse ecosystems |
| title | Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems |
| title_full | Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems |
| title_fullStr | Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems |
| title_full_unstemmed | Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems |
| title_short | Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems |
| title_sort | local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems |
| topic | random matrices sparse random graphs complex dynamical systems linear stability sparse ecosystems |
| url | https://doi.org/10.1088/2632-072X/ad2698 |
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