Pith Number

pith:CLIAMCS2

pith:2026:CLIAMCS2BH7VWCLC5BSC7GOWAG

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Symmetry breaking and high-dimensional chaos in sparse random networks of exact firing rate models

Pau Clusella

Directed sparse networks of exact firing rate models produce high-dimensional chaos in both excitatory and inhibitory populations.

arxiv:2605.15872 v1 · 2026-05-15 · nlin.CD · cond-mat.dis-nn · math.DS · nlin.AO

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Claims

C1strongest claim

Numerical simulations reveal that these hectic oscillatory states correspond to high-dimensional chaos with extensive properties.

C2weakest 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.

C3one 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.

References

91 extracted · 91 resolved · 1 Pith anchors

[1] Undirected networks In undirected networksΛ k ∈Rfor allk= 1, . . . , N. In excitatory populations (J >0), Eq. (6) shows that Re[λk]≤Re[λ 1]. Sinceλ 1 corresponds to a perturbation along the homoge- ne

[2] Using a Fisher Matrix framework, we have studied the frac- tional uncertaintiesσ θi /θi change for bothm dm · doi:10.13039/501100011033

[3] Let’s define the perturbation vector ζ= (δr 1, δv1,

[4] 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). This equation can be i

[5] (9) forµand Eq

Formal links

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Receipt and verification

First computed	2026-05-20T00:01:22.999954Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12d0060a5a09ff5b0962e8642f99d60194116fde28d021b26351282dbc3baea3

Aliases

arxiv: 2605.15872 · arxiv_version: 2605.15872v1 · doi: 10.48550/arxiv.2605.15872 · pith_short_12: CLIAMCS2BH7V · pith_short_16: CLIAMCS2BH7VWCLC · pith_short_8: CLIAMCS2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CLIAMCS2BH7VWCLC5BSC7GOWAG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 12d0060a5a09ff5b0962e8642f99d60194116fde28d021b26351282dbc3baea3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c968787b2fbd4dd38a91eb5f8263ce598a92eb836f6a7d098a34dcb117c87bdf",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "math.DS",
      "nlin.AO"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "nlin.CD",
    "submitted_at": "2026-05-15T11:44:07Z",
    "title_canon_sha256": "32a291eaea500fe0f3311d08956af34105814d2086720b2bc65b3c9631cc69fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15872",
    "kind": "arxiv",
    "version": 1
  }
}