Pith Number

pith:YYHODSXI

pith:2026:YYHODSXIA7POWWAP3CDOCIGHFA

not attested not anchored not stored refs resolved

Multi-cluster chimeras in phase oscillators with repulsive nonlocal coupling

Ayushi Saxena, Ram Ramaswamy, Sangeeta Rani Ujjwal

Phase oscillators with repulsive nonlocal coupling form multi-cluster chimeras where synchronized clusters differ by 2π/n.

arxiv:2605.15628 v1 · 2026-05-15 · nlin.AO

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Claims

C1strongest claim

In the multi-cluster chimera state the synchronized clusters are either antiphase or in splay with respect to each other, namely the n consecutive synchronized clusters differ in phase by 2π/n.

C2weakest assumption

The coupling function is assumed to be piecewise linear, nonlocal, repulsive, and to include a fixed phase lag; if the functional form or the nonlocality range changes, the reported phase-difference rule and stability regions may not hold.

C3one line summary

Nonlocal repulsive coupling produces multi-cluster chimeras with antiphase or splay synchronized clusters that differ by 2π/n, in contrast to attractive coupling, as shown by numerics, stability analysis, and Ott-Antonsen reduction.

References

58 extracted · 58 resolved · 0 Pith anchors

[1] G(x) -a a a a x FIG

[2] inverted Mexican- hat

[3] The interplay of the coupling function and the phase lag parameter α gives rise to various states

[4] 2(i)-(xxii)), for instance, Fig

[5] Therefore, the phase of the ith oscillator will evolve ac- cording to the following equation: ∂φ i ∂t = N∑ j=1 Gij sin(φ j − φ i − α )

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:08.921639Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c60ee1cae807deeb580fd886e120c7283f1c9696bf58a487c7c4b17c28d8fd98

Aliases

arxiv: 2605.15628 · arxiv_version: 2605.15628v1 · doi: 10.48550/arxiv.2605.15628 · pith_short_12: YYHODSXIA7PO · pith_short_16: YYHODSXIA7POWWAP · pith_short_8: YYHODSXI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YYHODSXIA7POWWAP3CDOCIGHFA \
  | 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: c60ee1cae807deeb580fd886e120c7283f1c9696bf58a487c7c4b17c28d8fd98

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5d3256cccd60b05afa1fb84eaef1757cd7d27f8a8e1fbb29149029078b77463",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.AO",
    "submitted_at": "2026-05-15T05:26:32Z",
    "title_canon_sha256": "8a7f32cf42bed50b94aee8f28a55f9bf2bc5a75bb996a224015fe8453d4ca589"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15628",
    "kind": "arxiv",
    "version": 1
  }
}