Pith. sign in

REVIEW 4 major objections 5 minor 30 references

Finite size effect in Kuramoto oscillators with inertia on simplicial complex

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Finite-size fluctuations induce a first-order synchronization transition in Kuramoto oscillators with inertia on 2-simplex complexes, even though the thermodynamic-limit analysis allows no forward transition; the critical coupling grows…

desk verdict A legitimate but quantitatively fragile extension of finite-size synchronization to inertial higher-order Kuramoto; the observed forward transition is real, but the reported power-law exponents rest on a fixed-time crossing rule and need a T-dependence check. read the letter →

arxiv 2506.23181 v1 pith:RHAXKXZW submitted 2025-06-29 nlin.AO

Manuel Lourenco , Abhishek Sharma , Priyanka Rajwani , Erick Alejandro Madrigal Solis , Mehrnaz Anvari , Sarika Jalan This is my paper · ORCID
classification nlin.AO MSC 34C1534D0682C26 PACS 05.45.Xt89.75.-k
keywords finite-sizeeffectsKuramotomodelinertiahigher-orderinteractionssimplicialcomplexsynchronizationtransitionorderparameterfluctuationspower-lawscaling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks what changes when a globally coupled Kuramoto model with inertia and triadic 2-simplex interactions is finite rather than infinite. The thermodynamic-limit analysis says that, starting from incoherence, there is no forward transition to synchronization at any coupling strength; only the backward path desynchronizes through a saddle-node bifurcation. The paper shows that finite size changes this picture: order-parameter fluctuations of size O(1/sqrt N) can carry the system over the unstable state that separates incoherence from synchronization, producing an abrupt first-order jump at a finite critical coupling K2c. Across network sizes from N=100 to N=5000, the paper finds K2c grows as a power law of N, with the exponent rising from 0.55 at m=0 to 0.73 at m=5, and larger inertia shifts K2c upward. If the claim is right, infinite-size predictions understate how easily triadic interactions synchronize real, finite oscillator systems, while inertia partially restores the infinite-size behavior.

What carries the argument

The load-bearing object is the unstable branch of the mean-field order-parameter dynamics, the separatrix between the stable incoherent state r1=0 and the stable synchronized state r1 approximately 1. For m=0 the paper derives the one-dimensional equation dr1/dt = -r1 + (K2/2)($r1^{3}$ - $r1^{5}$), whose three fixed points give this bistable geometry; for m>0 the same geometry is obtained from locked and drifting oscillator contributions. The mechanism is finite-size noise: r1 fluctuates with a width that decreases as O(1/sqrt N), and once fluctuations are large enough to reach the unstable separatrix, the system escapes to the synchronized branch. Coupling strength K2 controls the distance between the incoherent state and the separatrix, which is why larger K2 compensates for smaller fluctuations in larger systems.

What would settle it

Doubling or decupling the integration time and realization count and re-extracting K2c(N): if the threshold moves systematically with T, or if the log-log slope of K2c versus N changes, the reported power law is a finite-time artifact rather than a true scaling of the transition. A complementary check computes the Kramers escape rate over the unstable branch from the one-dimensional order-parameter dynamics and compares the predicted mean crossing time with the observed transition-time distribution.

Watch

Extended reading notes

Core claim

The central discovery is that a forward synchronization transition exists for finite Kuramoto networks with inertia and 2-simplex (triadic, three-body) coupling, even though the same model in the thermodynamic limit has no such transition. In the continuum limit the stable incoherent state r1=0 persists for all K2 in the forward direction, with an intermediate unstable branch and a stable synchronized branch appearing only in the bistable region; finite-size fluctuations of r1, whose width scales as O(1/sqrt N), let the system cross the unstable branch and settle on the synchronized state. The paper defines the forward critical coupling K2c as the smallest K2 for which at least one of 500 or 1000 realizations crosses to the synchronized branch within a fixed integration time T=200000, and reports K2c proportional to N^gamma with gamma = 0.55, 0.58, 0.67, and 0.73 for m = 0, 1, 2, and 5. The backward desynchronization threshold is unchanged by N or m, so increasing size and inertia both widen the hysteresis loop.

Load-bearing premise

The central result rests on treating the first crossing within a fixed simulation window of length T=200000 among 500 or 1000 realizations as the critical coupling; if longer runs or more realizations shift that crossing value, the reported power-law exponents are finite-time artifacts.

Editorial extensions

If this is right

  • For any finite globally coupled 2-simplex Kuramoto network starting from random phases, an abrupt forward jump to synchronization occurs at a finite coupling, contradicting the thermodynamic-limit prediction of no forward transition.
  • The critical coupling for this jump grows as a power law of network size, so larger systems need disproportionately stronger triadic coupling before fluctuations can trigger synchronization.
  • Adding inertia raises the critical coupling and increases the power-law exponent, meaning inertia acts as a stabilizing force that partly restores the infinite-size behavior in finite systems.
  • The backward transition point stays fixed with N and m, so hysteresis loops become wider as systems grow or as inertia increases.
  • The transition is an escape over an unstable state, so the waiting time to synchronization is distributed and shorter for larger K2, as the paper's transition-time statistics show.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the crossing event is reinterpreted as Kramers escape over the unstable branch, the same numerical data could test whether the mean transition time follows an exponential law and whether that law reproduces the reported exponents gamma(m) from a barrier-height calculation; the paper does not attempt this.
  • The fixed-time, few-realization definition of K2c likely makes the reported exponents sensitive to the observation window; redefining K2c through the rate of crossings at fixed K2 would provide a cleaner scaling and might change the prefactor, possibly the exponent.
  • For sparse or non-globally coupled simplicial complexes, the O(1/sqrt N) fluctuation scaling will be modified by degree heterogeneity and local topology, so the same mechanism should produce a different N-scaling of K2c; this is a testable extension.
  • The inertia-dependent exponent could be interpreted as inertia lowering the effective fluctuation temperature of the order parameter, which would connect the numerical exponents to an effective-noise model of the mean-field dynamics.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies the Kuramoto model with inertia and triadic (2-simplex) interactions on finite all-to-all networks. The authors report that, contrary to the thermodynamic-limit prediction of no forward synchronization transition, finite-size fluctuations cause an abrupt transition from the incoherent to the synchronized state at a finite coupling K2c. They further claim a power-law relation K2c ∝ N^γ with γ = 0.55, 0.58, 0.67, and 0.73 for m = 0, 1, 2, and 5, respectively, and that increasing inertia shifts K2c to larger values, counteracting finite-size effects. The explanation offered is that fluctuations in the order parameter, scaling as O(1/√N), allow the system to cross the unstable branch that separates incoherent and synchronized states in the bistable region.

Significance. If established, the result would be a useful cautionary example that thermodynamic-limit analyses of higher-order Kuramoto systems can miss finite-size-induced transitions, and the reported scaling of K2c with N and m would be a concrete quantitative prediction. The paper provides direct numerical evidence—time series and bimodal probability distributions in Figs. 1, 3, and 7—for finite-size-induced transitions in the bistable region, and the trend of K2c increasing with m is visually consistent across several system sizes. However, the headline power-law exponents are not yet demonstrated to be intrinsic model properties, and part of the analytical framework is imported from prior work. The manuscript does not ship machine-checked proofs or reproducible code, and the central quantitative claim currently rests on a single observational protocol with a fixed time horizon.

major comments (4)
  1. [Fig. 6 and accompanying text] The quantitative claim K2c ∝ N^γ in Fig. 6 rests on defining K2c as the smallest coupling at which at least one of 500 or 1000 realizations crosses to the synchronized branch within a fixed integration horizon T = 200000. Because the crossing is a rare fluctuation over the unstable intermediate branch (Figs. 1b and 1d), this measured threshold is effectively the coupling at which the first-passage time becomes comparable to T times the number of trials; for barrier-crossing dynamics such a threshold typically shifts logarithmically with T and with trial count, independent of any true critical coupling. The paper does not vary T, vary the number of trials, report error bars, or show that the inferred K2c has converged. The exponents γ = 0.55–0.73 may therefore be properties of the fixed observation window rather than of the model. I request a T-convergence study (e.g., K2c for T = 10^4, 10^5, 10^6 at fixed N and m) or an explicit argument that the finite-time crossing measure is asymptotically equivalent to a long-time critical coupling.
  2. [Fig. 6] The caption of Fig. 6 states that "the results have been normalized with respect to the network size," while the text and the axis labels treat the plotted values directly as K2c and fit K2c ∝ N^γ. If the ordinate is actually K2c/N or another normalized quantity, then the fitted slopes do not correspond to the claimed K2c scaling; if the ordinate is K2c, the caption is incorrect. The manuscript must clarify which quantity is plotted and, if normalization was applied, refit the power law accordingly. This ambiguity directly affects the headline exponents and must be resolved before the scaling claim can be evaluated.
  3. [Eqs. (5)–(6)] The m > 0 analytical curves used as black lines in Figs. 4 and 5 are imported from reference [20] without derivation; the text states "Following the further analytical derivation in [20]" and later notes that the drifting-oscillator integral in Eq. (6) is difficult to solve, with only the strong-synchronization case presented. Nevertheless, the paper's central explanation of the finite-size transition—that fluctuations must cross the intermediate unstable state—uses these imported curves to locate that unstable state. The authors should either derive the self-consistent equations for m ≠ 0 within this manuscript or clearly attribute the unstable branch to ref. [20] and justify why a thermodynamic-limit unstable branch is a valid reference for finite-N dynamics. This is load-bearing because the origin claim rests on the position of that branch.
  4. [Figs. 1(c), 3(a)] The paper repeatedly attributes the finite-size transition to fluctuations that scale as O(1/√N) and illustrates that the FWHM of P(r1) decreases with N, but it never quantifies this scaling. Since the power-law dependence of K2c on N is the headline result, a quantitative demonstration that the variance or FWHM indeed scales as 1/N (or at least as a known function of N) would directly support the proposed mechanism. I recommend adding such a scaling plot or analysis.
minor comments (5)
  1. [Figs. 2, 4, 5 and captions] Several figure captions contain rendering artifacts such as "/uni27E8" and "/uni27E9" (which should presumably be angle brackets), and the legend labels "f" and "b" are described as "postscript" rather than as subscripts. These should be corrected.
  2. [Analytical Derivation] The frequency distribution is called a "Lorenzian distribution" in the text; the correct spelling is "Lorentzian."
  3. [Model and Numerical Results] The paper states that the Runge-Kutta 4 method is used but does not give the time step dt, the total number of integration steps, or the initial phase/frequency sampling protocol beyond "random phases." These details are needed for reproducibility, especially because the crossing statistics depend on the integration horizon.
  4. [Fig. 2 caption] The caption says the analytical prediction of r1 is obtained "by solving Eq. A5 using bisection method," but Eq. A5 is a differential equation. It would be clearer to state that the fixed-point equation f(r1) = 0 is solved and that the dashed line is the unstable branch.
  5. [Introduction and references] The text cites "Tanaka et al. 9" for the critical point and then "Tanaka et al. 8" for the perturbation method, which is chronologically confusing; reorder the citations or adjust the text so the numerical order matches the discussion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the finite-size transition and the K2c–N power law are independent simulations, and the thermodynamic-limit analytics are either derived in-appendix or drawn from a separate published calculation.

full rationale

The central quantitative claim—the power-law K2c ∝ N^gamma in Fig. 6—is obtained by fitting log-log data from direct numerical integration of Eq. (3), not by evaluating the analytical formulas. The paper presents it as an empirical discovery ('We discover a power-law relationship...'), so no fitted input is renamed as a prediction. For m=0, the analytical branch is derived in Appendix A via the Ott-Antonsen ansatz from Eq. (A3), giving Eq. (A5) without using numerical data. For m≠0, Eqs. (5)-(6) are taken from ref. 20, a published calculation by a partially overlapping group; the current paper does not fit any of its simulation quantities into those formulas, and the numerical transition data (Figs. 2, 5, and 7) are generated independently, so the comparison is external validation rather than a circular reduction. The self-citations (refs. 20, 24, 27, and 30) are prior work with stated assumptions and are not invoked to forbid alternatives or to define the target result. Concerns about the fixed finite-time horizon T=200000 defining K2c and the 'normalized with respect to the network size' caption ambiguity are methodological validity issues, not instances where the claimed result is equivalent to its input by construction. No uniqueness theorem is imported, and no known empirical law is merely renamed. Hence there is no significant circularity.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central claim depends mainly on two fitted or chosen quantities: the power-law exponents gamma(m) and the finite-time horizon T used to define K2c. The analytical support relies on inherited assumptions from prior work rather than new derivation. No new physical entities are introduced.

free parameters (2)
  • Power-law exponent gamma(m) = gamma = 0.55 (m=0), 0.58 (m=1), 0.67 (m=2), 0.73 (m=5)
    Obtained by linear fit to log(K2c) versus log(N) in Fig. 6 for N = 100 to 5000. No error bars, fit diagnostics, or validation against other N ranges are reported.
  • Finite-time horizon T = 200000 = 200000 time units
    Transitions are counted only if they occur within T = 200000, as stated in the Fig. 3 caption and text. The reported K2c therefore depends on this chosen horizon and is not shown to be an asymptotic critical coupling.
assumptions (3)
  • standard math Ott-Antonsen ansatz reduction for m = 0 with Lorentzian frequency distribution
    Appendix A assumes the OA ansatz and Lorentzian g(omega) to derive Eq. (A5). This is a standard reduction, but it restricts the analytical claim to that distribution.
  • domain assumption Locked and drifting oscillator decomposition formulas, Eqs. (5) and (6), from reference [20] apply to the m > 0 system
    The paper states 'Following the further analytical derivation in [20]' and does not rederive these formulas. They inherit assumptions about which oscillators lock and which drift, and require a simultaneous self-consistent solution for r2 that is not shown.
  • domain assumption The thermodynamic-limit unstable branch acts as a fixed escape barrier for finite-N fluctuations
    The explanation of the finite-size transition assumes that fluctuations cross the unstable branch obtained from the N-to-infinity analysis. No fluctuation theory connects the measured r1 noise amplitude to the crossing rate or to the observed K2c scaling.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Finite size effect in Kuramoto oscillators with inertia on simplicial complex." pith.science (2026). https://pith.science/paper/RHAXKXZW

@misc{pith2026250623181,
  author       = {Pith},
  title        = {Pith review of: Finite size effect in Kuramoto oscillators with inertia on simplicial complex},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RHAXKXZW}},
  note         = {Machine review of arXiv:2506.23181}
}
read the original abstract

We investigate the finite-size effects on the dynamical evolution of the Kuramoto model with inertia coupled through triadic interactions. Our findings reveal that fluctuations resulting from the finite size drive the system toward a synchronized state at finite coupling, which contrasts with the analytical predictions {in thermodynamic limit} made for the same system. Building on the analytical calculations performed at the thermodynamic limit, we identify the origin of the synchronization transition that arises because of the finite size. We discover a power-law relationship between the network size and the critical coupling at which the first-order transition to synchronization occurs. Additionally, as inertia increases, there is a significant shift in the critical coupling toward higher values, indicating that inertia counteracts the effects caused by finite size.

Figures

Figures reproduced from arXiv: 2506.23181 by the authors.

Figure 1
Figure 1. FIG. 1. (a) and (b) plot the time series of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Variation of the order parameter [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Normalized probability density of [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The variation of mean order parameter [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Variation of the mean order parameter [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Critical coupling value [PITH_FULL_IMAGE:figures/full_fig_p004_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Time series of [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

30 extracted references · 29 canonical work pages

  1. [20]

    author author N. G. \ Sabhahit , author A. S. \ Khurd , \ and\ author S. Jalan ,\ title title Prolonged hysteresis in the kuramoto model with inertia and higher-order interactions , \ @noop journal journal Physical Review E \ volume 109 ,\ pages 024212 ( year 2024 a ) NoStop

    work page 2024

  2. [1]

    Buck ,\ title title Synchronous rhythmic flashing of fireflies

    author author J. Buck ,\ title title Synchronous rhythmic flashing of fireflies. ii. \ @noop journal journal The Quarterly review of biology \ volume 63 ,\ pages 265--289 ( year 1988 ) NoStop

    work page 1988

  3. [2]

    author author T. J. \ Walker ,\ title title Acoustic synchrony: two mechanisms in the snowy tree cricket , \ @noop journal journal Science \ volume 166 ,\ pages 891--894 ( year 1969 ) NoStop

    work page 1969

  4. [3]

    Attanasi , author A

    author author A. Attanasi , author A. Cavagna , author L. Del Castello , author I. Giardina , author A. Jelic , author S. Melillo , author L. Parisi , author O. Pohl , author E. Shen , \ and\ author M. Viale ,\ title title Emergence of collective changes in travel direction of starling flocks from individual birds' fluctuations , \ @noop journal journal J...

    work page 2015

  5. [4]

    author author G. V. \ Osipov , author J. Kurths , \ and\ author C. Zhou ,\ @noop title Synchronization in oscillatory networks \ ( publisher Springer Science & Business Media ,\ year 2007 ) NoStop

    work page 2007

  6. [5]

    author author Y. Kuramoto ,\ title title Self-entrainment of a population of coupled non-linear oscillators , \ in\ @noop booktitle International Symposium on Mathematical Problems in Theoretical Physics: January 23--29, 1975, Kyoto University, Kyoto/Japan \ ( organization Springer ,\ year 1975 )\ pp.\ pages 420--422 NoStop

    work page 1975

  7. [6]

    author author S. H. \ Strogatz ,\ title title From kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators , \ @noop journal journal Physica D: Nonlinear Phenomena \ volume 143 ,\ pages 1--20 ( year 2000 ) NoStop

    work page 2000

  8. [7]

    author author B. Ermentrout ,\ title title An adaptive model for synchrony in the firefly Pteroptyx malaccae , \ @noop journal journal Journal of Mathematical Biologye \ volume 29 ( year 1991 ) NoStop

    work page 1991

Show all 30 references
  1. [8]

    \ Tanaka , author A

    author author H.-A. \ Tanaka , author A. J. \ Lichtenberg , \ and\ author S. Oishi ,\ title title First Order Phase Transition Resulting from Finite Inertia in Coupled Oscillator Systems , \ @noop journal journal Phys. Rev. Lett. \ volume 78 ,\ pages 2104--2107 ( year 1997 a ) NoStop

    1997

  2. [9]

    \ Tanaka , author A

    author author H.-A. \ Tanaka , author A. J. \ Lichtenberg , \ and\ author S. Oishi ,\ title title Self-synchronization of coupled oscillators with hysteretic responses , \ @noop journal journal Physica D: Nonlinear Phenomena \ volume 100 ,\ pages 279--300 ( year 1997 b ) NoStop

    1997

  3. [10]

    Ji , author T

    author author P. Ji , author T. K. D. \ Peron , author P. J. \ Menck , author F. A. \ Rodrigues , \ and\ author J. Kurths ,\ title title Cluster explosive synchronization in complex networks , \ @noop journal journal Phys. Rev. Lett. \ volume 110 ,\ pages 218701 ( year 2013 ) NoStop

    2013

  4. [11]

    author author B. R. \ Trees , author V. Saranathan , \ and\ author D. Stroud ,\ title title Synchronization in disordered josephson junction arrays: Small-world connections and the kuramoto model , \ @noop journal journal Phys. Rev. E \ volume 71 ,\ pages 016215 ( year 2005 ) NoStop

    2005

  5. [12]

    author author J. M. V. \ Grzybowski , author E. E. N. \ Macau , \ and\ author T. Yoneyama ,\ title title On synchronization in power-grids modelled as networks of second-order Kuramoto oscillators , \ @noop journal journal Chaos: An Interdisciplinary Journal of Nonlinear Scien...

    2016

  6. [13]

    Dörfler , author M

    author author F. Dörfler , author M. Chertkov , \ and\ author F. Bullo ,\ title title Synchronization in complex oscillator networks and smart grids , \ @noop journal journal Proceedings of the National Academy of Sciences \ volume 110 ,\ pages 2005--2010 ( year 2013 ) NoStop

    2005

  7. [14]

    Rohden , author A

    author author M. Rohden , author A. Sorge , author M. Timme , \ and\ author D. Witthaut ,\ title title Self-organized synchronization in decentralized power grids , \ @noop journal journal Phys. Rev. Lett. \ volume 109 ,\ pages 064101 ( year 2012 ) NoStop

    2012

  8. [15]

    Witthaut , author F

    author author D. Witthaut , author F. Hellmann , author J. Kurths , author S. Kettemann , author H. Meyer-Ortmanns , \ and\ author M. Timme ,\ title title Collective nonlinear dynamics and self-organization in decentralized power grids , \ @noop journal journal Rev. Mod. Phys....

    2022

  9. [16]

    author author P. S. \ Skardal \ and\ author A. Arenas ,\ title title Abrupt desynchronization and extensive multistability in globally coupled oscillator simplexes , \ @noop journal journal Physical review letters \ volume 122 ,\ pages 248301 ( year 2019 ) NoStop

    2019

  10. [17]

    \ Lord , author P

    author author L.-D. \ Lord , author P. Expert , author H. M. \ Fernandes , author G. Petri , author T. J. \ Van Hartevelt , author F. Vaccarino , author G. Deco , author F. Turkheimer , \ and\ author M. L. \ Kringelbach ,\ title title Insights into brain architectures from the...

    2016

  11. [18]

    Estrada \ and\ author G

    author author E. Estrada \ and\ author G. J. \ Ross ,\ title title Centralities in simplicial complexes. applications to protein interaction networks , \ @noop journal journal Journal of theoretical biology \ volume 438 ,\ pages 46--60 ( year 2018 ) NoStop

    2018

  12. [19]

    Grilli , author G

    author author J. Grilli , author G. Barab \'a s , author M. J. \ Michalska-Smith , \ and\ author S. Allesina ,\ title title Higher-order interactions stabilize dynamics in competitive network models , \ @noop journal journal Nature \ volume 548 ,\ pages 210--213 ( year 2017 ) NoStop

    2017

  13. [21]

    author author H. Daido ,\ title title Scaling behaviour at the onset of mutual entrainment in a population of interacting oscillators , \ @noop journal journal Journal of Physics A: Mathematical and General \ volume 20 ,\ pages L629 ( year 1987 ) NoStop

    1987

  14. [22]

    author author H. Daido ,\ title title Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators , \ @noop journal journal Journal of Statistical Physics \ volume 60 ( year 1990 ) NoStop

    1990

  15. [23]

    author author H. Daido ,\ title title Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions: bifurcation of the order function , \ @noop journal journal Physica D: Nonlinear Phenomena \ volume 91 ,\ pages 24--66 ( year 1996 ) NoStop

    1996

  16. [24]

    Suman \ and\ author S

    author author A. Suman \ and\ author S. Jalan ,\ title title Finite-size effect in kuramoto oscillators with higher-order interactions , \ @noop journal journal Chaos: An Interdisciplinary Journal of Nonlinear Science \ volume 34 ( year 2024 ) NoStop

    2024

  17. [25]

    Gao \ and\ author K

    author author J. Gao \ and\ author K. Efstathiou ,\ title title Self-consistent method and steady states of second-order oscillators , \ @noop journal journal Physical Review E \ volume 98 ,\ pages 042201 ( year 2018 ) NoStop

    2018

  18. [26]

    author author P. S. \ Skardal \ and\ author A. Arenas ,\ title title Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching , \ @noop journal journal Communications Physics \ volume 3 ,\ pages 218 ( year 2020 ) NoStop

    2020

  19. [27]

    author author A. D. \ Kachhvah \ and\ author S. Jalan ,\ title title Hebbian plasticity rules abrupt desynchronization in pure simplicial complexes , \ @noop journal journal New Journal of Physics \ volume 24 ,\ pages 052002 ( year 2022 ) NoStop

    2022

  20. [28]

    author author N. G. \ Sabhahit , author A. S. \ Khurd , \ and\ author S. Jalan ,\ title title Prolonged hysteresis in the kuramoto model with inertia and higher-order interactions , \ @noop journal journal Phys. Rev. E \ volume 109 ,\ pages 024212 ( year 2024 b ) NoStop

    2024

  21. [29]

    Ott \ and\ author T

    author author E. Ott \ and\ author T. M. \ Antonsen ,\ title title Low dimensional behavior of large systems of globally coupled oscillators , \ @noop journal journal Chaos: An Interdisciplinary Journal of Nonlinear Science \ volume 18 ,\ pages 037113 ( year 2008 ) NoStop

    2008

  22. [30]

    Sharma , author P

    author author A. Sharma , author P. Rajwani , \ and\ author S. Jalan ,\ title title Synchronization transitions in adaptive Kuramoto–Sakaguchi oscillators with higher-order interactions , \ @noop journal journal Chaos: An Interdisciplinary Journal of Nonlinear Science \ volume...

    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.