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Evolutionary Kuramoto dynamics unravels origins of chimera states in neural populations.

Code ↔ Paper

6 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 6 matches · 2 of them tie a paragraph to a whole file, not to given lines: weak matches, whose lines are not tinted
  1. [1] § 4 Methods › 4.5 Game type nomenclature ↔ src/julia/game_taxonomy.jl, the whole file · a weak match · score 0.95 · double tie, high tie, double coordination, high harmony, symmetric game, payoff matrix
  2. [2] § 4 Methods › 4.3 Birth-death Moran process ↔ src/julia/moran.jl, lines 145–205 · score 0.90 · death node, exponential fitness, reproduction graph, edge weight, birth, interaction graph
  3. [3] § 4 Methods › 4.5 Game type nomenclature ↔ src/julia/postprocess.jl, lines 444–497 · score 0.72 · binomial nomenclature, payoff matrix, ordinal, ties, taxonomy, symmetric
  4. [4] § 4 Methods › 4.2 Population setup ↔ src/julia/utils.jl, lines 52–135 · score 0.67 · dangling node, reproduction graph, interaction graph, loop, edges, elegans
  5. [5] § 4 Methods › 4.6 Plurality game type ↔ src/julia/moran.jl, lines 145–205 · score 0.57 · edge weight, payoff matrix, interaction graph, CN, phase, players
  6. [6] § 2 Results › 2.2 Parameter space ↔ src/julia/game_taxonomy.jl, the whole file · a weak match · score 0.55 · snowdrift, swapped, prisoner, double, concord, harmony

Paper

Loaded from Europe PMC by your browser, not stored by OSCR: doi.org · Europe PMC

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The authors' code

Julia · 73 lines · 3.9 KB · GPL-3.0 · 2 matches

  1. # SPDX-License-Identifier: GPL-3.0-or-later
  3. @enum GameType chicken battle hero compromise deadlock dilemma staghunt assurance coordination peace harmony concord neutral allCommunicative allNoncommunicative disconnectedSynchronizedPopulations
  5. @enum TieType lowTie midTie highTie doubleTie tripleTie basicTie zeroTie
  7. const game_type_full_names = Dict(chicken => "Snowdrift", # Also called chicken
  8. battle => "Battle of the Sexes",
  9. hero => "Hero",
  10. compromise => "Compromise",
  11. deadlock => "Deadlock",
  12. dilemma => "Prisoner's Dilemma",
  13. staghunt => "Mutualism", # Also called Staghunt
  14. assurance => "Assurance",
  15. coordination => "Coordination",
  16. peace => "Peace",
  17. harmony => "Harmony",
  18. concord => "Concord",
  19. neutral => "Neutral",
  20. )
  22. # Source: doi:10.3390/g6040495
  23. # In left-up convention (modified from right-up convention by swapping columns)
  24. # = means exactly the same payoff matrix, \approx means equivalent up to swap_strategies!
  25. const game_taxonomy = Dict(
  26. [4 2;3 1] => (missing, concord),
  27. [4 3;2 1] => (missing, harmony),
  28. [4 3;1 2] => (missing, peace),
  29. [4 2;1 3] => (missing, coordination),
  30. [4 1;2 3] => (missing, assurance),
  31. [4 1;3 2] => (missing, staghunt),
  32. [3 1;4 2] => (missing, dilemma),
  33. [2 1;4 3] => (missing, deadlock),
  34. [1 2;4 3] => (missing, compromise),
  35. [1 3;4 2] => (missing, hero),
  36. [2 3;4 1] => (missing, battle),
  37. [3 2;4 1] => (missing, chicken),
  38. [2 3;4 2] => (lowTie, battle),
  39. [2 2;4 3] => (lowTie, deadlock),
  40. [3 2;4 2] => (lowTie, dilemma),
  41. [4 2;2 3] => (lowTie, coordination),
  42. [4 3;2 2] => (lowTie, harmony),
  43. [4 2;3 2] => (lowTie, concord),
  44. [3 3;4 1] => (midTie, battle),
  45. [1 3;4 3] => (midTie, compromise),
  46. [3 1;4 3] => (midTie, deadlock),
  47. [4 1;3 3] => (midTie, staghunt),
  48. [4 3;1 3] => (midTie, peace),
  49. [4 3;3 1] => (midTie, harmony),
  50. [1 4;4 2] => (highTie, hero),
  51. [2 4;4 1] => (highTie, hero), # high battle \approx high hero
  52. [4 2;4 1] => (highTie, concord), # = high chicken
  53. [4 1;4 2] => (highTie, staghunt), # = high dilemma
  54. [4 2;1 4] => (highTie, coordination),
  55. [4 1;2 4] => (highTie, coordination), # high assurance \approx high coord
  56. [4 4;1 2] => (highTie, peace),
  57. [2 1;4 4] => (highTie, peace), # high deadlock \approx high peace
  58. [4 4;2 1] => (highTie, harmony),
  59. [1 2;4 4] => (highTie, harmony), # high compromise \approx high harmony
  60. [4 2;4 2] => (doubleTie, staghunt), # = double dilemma; note: bruns2015 claims double dilemma = double dilemma, which is tautologically true, but (correctly) states double dilemma = double staghunt elsewhere
  61. [4 2;2 4] => (doubleTie, coordination),
  62. [2 4;4 2] => (doubleTie, coordination), # double hero \approx double coordination; note: this is the only equivalent pair that is not related by swap_strategies!;
  63. # Instead, they are related by swapping only the columns or rows, but not both. Usually, doing this produces a non-symmetric game, but it this case, it is still symmetric
  64. [4 4;2 2] => (doubleTie, harmony),
  65. [2 2;4 4] => (doubleTie, harmony), # double compromise \approx double harmony
  66. [4 4;1 4] => (tripleTie, deadlock),
  67. [4 1;4 4] => (tripleTie, deadlock), # note: not explicitly given in bruns2015, but equivalent under swap_strategies!
  68. [4 4;4 1] => (tripleTie, harmony),
  69. [1 4;4 4] => (tripleTie, harmony), # note: not explicitly given in bruns2015, but equivalent under swap_strategies!
  70. [3 3;4 3] => (basicTie, dilemma),
  71. [4 3;3 3] => (basicTie, harmony),
  72. [4 4;4 4] => (zeroTie, neutral),
  73. )

game_taxonomy.jl at commit 1f1418f, under GPL-3.0 · at the source

Overview

Authors: Thomas Zdyrski1, Scott Pauls1, Feng Fu1,2
ORCID iDs: Thomas Zdyrski, Feng Fu
  1. Department of Mathematics, Dartmouth College, Hanover, New Hampshire, United States of America
  2. Department of Biomedical Data Science, Geisel School of Medicine at Dartmouth, Hanover, New Hampshire, United States of America
Institutions: Dartmouth College (United States)
Journal: PLoS computational biology, volume 22, issue 4, article e1014214
Dates: received 11 November 2025; accepted 9 April 2026; published online 30 April 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1371/journal.pcbi.1014214 · PMID 42060713 · PMCID PMC13152215 · OpenAlex W4414806760
Open access: gold, a free copy (OpenAlex)
Preprint: arxiv:2510.00423
Status: code verified
Categories: computational modeling (no new data) (modality), human (organism), C. elegans (organism)
Methods: Connectivity
MeSH: Biological Evolution*, Models, Neurological*, Nerve Net*, Neurons*, Animals, Brain, Computational Biology, Computer Simulation, Connectome, Game Theory, Humans (* major topic)
Topic: Nonlinear Dynamics and Pattern Formation (Computer Networks and Communications, Computer Science), according to OpenAlex
Citations: not cited yet (Europe PMC); 33 references in the paper

Abstract

Neural synchronization is central to cognition. However, incomplete synchronization often produces chimera states, where coherent and incoherent dynamics coexist. Recent studies have suggested that these chimera states could be important in human cognitive organization. In particular, chimera states have been suggested as a regulator of cognitive integration and regulation with varying quality as humans age. While previous studies have explored such chimera states using networks of coupled oscillators, it remains unclear why neurons commit to communication or how chimera states persist. Here, we investigate the coevolution of neuronal phases and communication strategies on directed, weighted networks where interaction payoffs depend on phase alignment and may be asymmetric due to unilateral communication. The graph structure enables us to apply a game-theoretic model of Kuramoto-like oscillators to brain connectomes, and the asymmetry captures biochemical differences between communicative and non-communicative neurons. Combined, these two generalizations enable us to apply the computationally-tractable game-theoretic model of Kuramoto models to realistic brain networks and analyze the role of connectome structure on neuron communication. We find that both connection weights and directionality influence the stability of communicative strategies—and, consequently, full synchronization—as well as the strategic nature of neuronal interactions. Applying our framework to the C. elegans connectome, we show that emergent payoff structures, such as the staghunt game, control population dynamics. We demonstrate that weighted, directed connectivity in the Caenorhabditis elegans (C. elegans) connectome is sufficient to generate robust chimera states modulated by payoff asymmetries. Our computational results demonstrate a promising neurogame-theoretic perspective, leveraging evolutionary graph theory to shed light on mechanisms of neuronal coordination beyond classical synchronization models.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repositories

Its files are read in the Code ↔ Paper reader above, with 6 matches between paragraphs and lines of code.

tzdyrski.github.io/egt-kuramoto

License: none: the authors keep all their rights
State: the link answers, verified on 30 September 2026
Evidence: the link answers
Software Heritage: not checked
Found in: “Data Availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 30 September 2026: the link answers (HTTP 200)
  • 30 September 2026: the link answers (HTTP 200)
At the source: tzdyrski.github.io/egt-kuramoto/notebooks/EKT_Plots.html

tzdyrski/egt-kuramoto

License: GPL-3.0
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Commit: 1f1418f22644588eac687450f68f16c48f7efc97, 14 April 2026
Languages: Julia (31)
Size: 133 files, 31 scripts
Software Heritage: not archived
Found in: “Data Availability”
Holds: README, license file, environment (Manifest.toml, Project.toml, test/Project.toml), tests, continuous integration
Not found: CITATION.cff, documentation
Tools: DataFrames.jl (2 files), Makie (2 files)
Availability: 1 check, the latest on 30 September 2026: the link answers
  • 30 September 2026: the link answers
33 files
At the source: github.com/TZdyrski/egt-kuramoto/tree/1.1.1

Zenodo 19582421

License: GPL-3.0
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: “Data Availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: DataFrames.jl (2 files), Makie (2 files)
Availability: 1 check, the latest on 30 September 2026: the link answers (HTTP 200)
  • 30 September 2026: the link answers (HTTP 200)
33 files
At the source: doi.org/10.5281/zenodo.19582421

The paper's code and data availability statement is in the Data section.

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  • 3 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 62 scripts, each with its path and the digest of its content;
  • 6 matches between paragraphs of the paper and lines of the code (method lexical-v1);
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Data

Datasets cited

Data Availability

The raw and processed data for all simulated parameter ranges is available on Zenodo at https://doi.org/10.5281/zenodo.19235754. An interactive webpage for exploring the data set is available at https://tzdyrski.github.io/egt-kuramoto/notebooks/EKT_Plots.html. Additionally, all source code is available via GitHub at https://github.com/TZdyrski/egt-kuramoto/tree/1.1.1 or Zenodo at https://doi.org/10.5281/zenodo.19582421.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 11 MeSH terms, 32 references.

Cite

This paper

Zdyrski, T., Pauls, S., & Fu, F. (2026). Evolutionary Kuramoto dynamics unravels origins of chimera states in neural populations. PLoS computational biology, 22(4), e1014214. https://doi.org/10.1371/journal.pcbi.1014214

BibTeX

@article{zdyrski2026evolutionary,
author = {Zdyrski, Thomas and Pauls, Scott and Fu, Feng},
title = {{Evolutionary Kuramoto dynamics unravels origins of chimera states in neural populations}},
journal = {PLoS computational biology},
year = {2026},
month = apr,
volume = {22},
number = {4},
pages = {e1014214},
publisher = {PLOS},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1014214},
url = {https://doi.org/10.1371/journal.pcbi.1014214},
pmid = {42060713},
pmcid = {PMC13152215}
}

RIS

TY - JOUR
AU - Zdyrski, Thomas
AU - Pauls, Scott
AU - Fu, Feng
TI - Evolutionary Kuramoto dynamics unravels origins of chimera states in neural populations
T2 - PLoS computational biology
J2 - PLoS Comput Biol
PY - 2026
DA - 2026/04/30
VL - 22
IS - 4
SP - e1014214
SN - 1553-734X
PB - PLOS
DO - 10.1371/journal.pcbi.1014214
UR - https://doi.org/10.1371/journal.pcbi.1014214
LA - en
ER -

CSL-JSON

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