{"paper":{"title":"Symmetry breaking and high-dimensional chaos in sparse random networks of exact firing rate models","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Directed sparse networks of exact firing rate models produce high-dimensional chaos in both excitatory and inhibitory populations.","cross_cats":["cond-mat.dis-nn","math.DS","nlin.AO"],"primary_cat":"nlin.CD","authors_text":"Pau Clusella","submitted_at":"2026-05-15T11:44:07Z","abstract_excerpt":"Exact firing rate models, also known as next-generation neural mass models (NG-NMMs), provide a rigorous description of the dynamics of neural populations. While in its simplest form a single population only displays fixed-point activity, multi-population models may display a range of different behaviors. In this work, we study the dynamics of all-excitatory or all-inhibitory NG-NMMs coupled through sparse random networks with row-normalized network topology. Linear stability analysis of the homogeneous states of the system, representing asynchronous neural activity, provides a dispersion rela"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Numerical simulations reveal that these hectic oscillatory states correspond to high-dimensional chaos with extensive properties.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that bounds from random matrix theory accurately identify instability regions for the spectra of row-normalized sparse random connectivity matrices in both directed and undirected cases.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Linear stability analysis of homogeneous states in sparse random networks of next-generation neural mass models links instabilities to connectivity spectra, revealing winner-takes-all patterns in undirected inhibitory systems and high-dimensional chaos in directed networks.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Directed sparse networks of exact firing rate models produce high-dimensional chaos in both excitatory and inhibitory populations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7e1d1f340d53e410a8a22b8475ca5b93b309982cde3bd3a71be0648b3f207229"},"source":{"id":"2605.15872","kind":"arxiv","version":1},"verdict":{"id":"be98eaf1-17be-4f25-acbd-b7e98278e00c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:30:22.760909Z","strongest_claim":"Numerical simulations reveal that these hectic oscillatory states correspond to high-dimensional chaos with extensive properties.","one_line_summary":"Linear stability analysis of homogeneous states in sparse random networks of next-generation neural mass models links instabilities to connectivity spectra, revealing winner-takes-all patterns in undirected inhibitory systems and high-dimensional chaos in directed networks.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that bounds from random matrix theory accurately identify instability regions for the spectra of row-normalized sparse random connectivity matrices in both directed and undirected cases.","pith_extraction_headline":"Directed sparse networks of exact firing rate models produce high-dimensional chaos in both excitatory and inhibitory populations."},"integrity":{"clean":false,"summary":{"advisory":1,"critical":0,"by_detector":{"doi_compliance":{"total":1,"advisory":1,"critical":0,"informational":0}},"informational":0},"endpoint":"/pith/2605.15872/integrity.json","findings":[{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. 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In excitatory populations (J >0), Eq. (6) shows that Re[λk]≤Re[λ 1]. Sinceλ 1 corresponds to a perturbation along the homoge- ne","work_id":"30bb37c7-ff93-4ad7-b3b4-a86e85209484","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.13039/501100011033","year":null,"title":"Using a Fisher Matrix framework, we have studied the frac- tional uncertaintiesσ θi /θi change for bothm dm","work_id":"dd544aa1-fa7d-44a2-9d86-6421740a1e1e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Let’s define the perturbation vector ζ= (δr 1, δv1,","work_id":"b4cda448-0fae-450c-b309-c8f2217a3bd8","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Homogeneous system The stability of homogeneous fixed point to homogeneous perturbations is given byΛ1 = 1in Eq. (6). SettingRe[λ ± 1 ] = 0provides J= ∆2 2π2(τ r0)3 + 2π2(τ r0). 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