Pith. sign in

REVIEW 2 major objections 5 minor 68 references

The role of inhibitory neuronal variability in modulating phase diversity between coupled networks

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read The paper argues that the composition of inhibitory neuron types in a receiver population—fast-spiking versus low-threshold-spiking—determines the phase relationship between two unidirectionally coupled cortical-like networks, and that…

desk verdict Solid and genuinely new observations on how FS/LTS inhibitory composition controls DS-AS transition routes, but the proposed period-ratio mechanism is post-hoc and should be tested or demoted. read the letter →

arxiv 2411.19664 v1 pith:N2QHKH4F submitted 2024-11-29 q-bio.NC physics.bio-ph

Katiele V. P. Brito , Joana M. G. L. Silva , Claudio R. Mirasso , Fernanda S. Matias This is my paper · ORCID
classification q-bio.NCphysics.bio-ph PACS 87.18.Sn87.19.ll87.19.lm
keywords neuronalheterogeneityinhibitoryneuronsfast-spikinglow-threshold-spikingphasediversityanticipatedsynchronizationbistabilityzero-lag
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 studies two coupled populations of spiking neurons, a sender and a receiver, and asks whether the known diversity of inhibitory neurons changes how the two populations lock in phase. It claims that the local mix of fast-spiking (FS) and low-threshold-spiking (LTS) inhibitory neurons in the receiver is an active control parameter: depending on this mix, the receiver can lag behind the sender (delayed synchronization), fire ahead of the sender (anticipated synchronization), fire at zero lag, or switch unpredictably between lag and anticipation (phase bistability). The paper further claims that inhibitory heterogeneity enlarges the regions of zero-lag and bistable behavior, and that the route from delayed to anticipated synchronization—via zero lag or via bistability—is set by whether the uncoupled receiver's free-running period is already shorter than the sender's or crosses it. If true, this gives a mechanistic role to inhibitory cell-type diversity in determining how distant brain areas communicate through oscillations.

What carries the argument

The central object is a sender-receiver motif of two Izhikevich spiking-neuron populations coupled unidirectionally by excitatory chemical synapses, with local inhibitory feedback conductance gI. Within this motif, neuronal heterogeneity is controlled by the parameter Xi, which shifts the distribution of the Izhikevich parameters (a,b) for inhibitory neurons between fast-spiking (a = 0.10, b = 0.20) and low-threshold-spiking (a = 0.02, b = 0.25) types, and by X, which shifts excitatory types among regular-spiking, chattering, and intrinsically bursting neurons. The observable that carries the argument is the mean time delay τ between the peaks of the two populations' mean membrane potentials: positive τ defines delayed synchronization, negative τ defines anticipated synchronization, near-zero τ defines zero-lag synchronization, and a bi-Gaussian distribution of cycle-to-cycle delays defines phase bistability. The proposed mechanism for the DS-AS route compares the free-running periods TS (sender) and TR (uncoupled receiver, gE = 0): bistability arises when TR < TS already in the DS regime, and zero-lag transitions occur where the period curves cross, TR = TS.

What would settle it

Simulate the coupled motif across a dense grid of (Xi, gI, X) and compare the DS-AS transition route with the sign of TR - TS from the corresponding uncoupled simulations; find one parameter point where TR < TS throughout the DS regime yet the transition goes through zero-lag synchronization rather than bistability, or where TR = TS yet the transition is bistable, either of which would contradict the proposed period-relation rule.

Watch

Extended reading notes

Core claim

The central discovery is that changing the distribution of inhibitory neuron types at the receiver—from all fast-spiking to all low-threshold-spiking, and through the intermediate heterogeneous mixtures controlled by the parameter Xi—changes the phase-locking regime between the sender and receiver populations. Both homogeneous inhibitory networks can show delayed synchronization, anticipated synchronization, and phase bistability, and the all-LTS network additionally shows zero-lag synchronization. As Xi is varied, the system can transition from DS to AS through either a bistable phase (at lower inhibitory conductance, gI = 4 nS) or through zero-lag synchronization (at higher gI = 6 nS), and the paper relates this route to the free-running periods: when the receiver remains faster than the sender through the DS regime, the transition is via bistability; when the receiver's free-running period crosses the sender's, the transition is via zero-lag. The paper presents this period-relation rule as a suggested mechanism rather than a derivation from the coupled equations.

Load-bearing premise

The paper's mechanistic explanation rests on the premise that the free-running periods measured with the coupling turned off (gE = 0) continue to dictate the transition route once the coupling is turned on, a relation inferred from a limited set of parameter points rather than derived from the coupled equations.

Editorial extensions

If this is right

  • The local proportion of FS versus LTS inhibitory neurons becomes a candidate control parameter for inter-area phase relations, complementing coupling strength and propagation delay.
  • Changing the inhibitory cell-type composition of a receiver population should shift the system from delayed to anticipated synchronization, with the transition route (zero-lag or bistable) tracking the free-running period relation.
  • In bistable regimes, cycle-to-cycle phase differences alternate between positive and negative values, so short observation windows would misclassify the regime as purely DS or purely AS.
  • The enlargement of zero-lag and bistable regions by heterogeneity implies that neuronal variability can promote, rather than merely disrupt, coherent phase relations between coupled populations.
  • Anticipation times in this model emerge from heterogeneity rather than being imposed by hard-wired delayed self-feedback.

Reading between the lines

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

  • Beyond the paper's claims: because the period-relation rule is inferred from comparing coupled and uncoupled simulations at selected parameter points, a natural next step is to map the TR = TS surface across the full (Xi, gI, X) parameter space and test whether the zero-lag/bistability boundary tracks that surface exactly; this would turn a suggested correlation into a predictive law.
  • Beyond the paper's claims: if the FS/LTS ratio acts this way in vivo, optogenetically shifting the inhibitory cell-type balance in one cortical area should measurably change its phase lag relative to a connected area, providing a direct experimental test.
  • Beyond the paper's claims: the slow alternation between DS and AS in the bistable regime could, if the mechanism generalizes, serve as a substrate for perceptual rivalry and other switch-like cognitive states, because the phase difference itself would carry the switching information.
  • Beyond the paper's claims: extending the two-population motif to a chain of areas, each node's inhibitory composition could set its phase relation to the next and thereby route information directionally without changing connection strengths.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper studies a motif of two unidirectionally coupled Izhikevich spiking networks, a sender and a receiver, and investigates how the composition of inhibitory neuron types (fast-spiking vs. low-threshold-spiking) in the receiver affects the phase relationship between the two populations. By varying the inhibitory heterogeneity parameter Xi, the excitatory heterogeneity X, and the inhibitory conductance gI, the simulations produce delayed synchronization (DS), anticipated synchronization (AS), zero-lag synchronization (ZL), and a bistable regime (BI) that alternates between DS and AS. The authors compare homogeneous only-FS and only-LTS receivers, map the regimes in parameter space, and propose in Sec. III.D that the route of the DS-AS transition is determined by the uncoupled free-running period of the receiver relative to the sender: bistability occurs when the receiver is already faster in the DS regime, while zero-lag occurs when the free-running periods cross.

Significance. If the reported observations are robust, the paper makes a useful contribution by showing that local inhibitory cell-type composition, not just coupling strength, can control inter-areal phase diversity in a biologically plausible model class. The extensive time-series examples, delay histograms, and parameter scans provide a clear phenomenology of DS, AS, ZL, and BI regimes, and the comparison between only-FS and only-LTS networks is a natural and instructive design. The strength of the paper is the demonstration that phase diversity, including anticipating synchronization and bistability, arises in a spiking network model with heterogeneous inhibitory neurons, which had not been shown before. The main weakness is that the mechanistic rule proposed in Sec. III.D is post-hoc and untested, and the prominent claim that heterogeneity 'enlarges' the zero-lag and bistability regions rests on a visual comparison without statistical support. With additional quantitative analysis, the contribution could be significant for understanding how local inhibitory variability shapes communication between cortical areas; as it stands, the paper is more descriptive than explanatory.

major comments (2)
  1. [Sec. III.D, Figs. 11-12] The proposed mechanism for the DS-AS transition route is not established. The rule that bistability occurs when the free-running receiver period is already shorter than the sender's (TR < TS in the DS regime) and that zero-lag occurs when TR = TS is inferred by comparing gE = 0 simulations with gE = 0.5 nS coupled simulations at a small set of parameter values. However, in the coupled regime each receiver neuron receives 20 excitatory synapses from the sender (Sec. II.C), which can alter the receiver's effective oscillation period. The uncoupled period relation may therefore not persist once coupling is switched on, and the paper provides neither a derivation from the coupled equations nor a systematic test of the rule across the parameter space. The comparison covers only a few horizontal slices (e.g., gI = 4.0 and 6.0 nS, X in a narrow range), and no statistical measure is given for how well the period relation predicts the observed route. Because the concluding remarks state that the mechanism has been demonstrated, this post-hoc, untested rule is load-bearing and requires either a direct test (e.g., computing the effective receiver period under coupling and checking the prediction over the full (X, Xi, gI) grid) or an explicit reframing as a heuristic observation that is not part of the paper's central claims.
  2. [Sec. III.C, Fig. 9(g)] The claim that inhibitory heterogeneity 'enlarges the region of zero-lag synchronization and bistability' (Abstract and Sec. III.C) is supported only by a visual comparison of the widths of the green region at Xi ≈ 0.1 and Xi = −0.04 in Fig. 9(g). This is a single qualitative comparison with no error bars, no bootstrapped region boundaries, and no quantitative definition of what constitutes an enlargement. The phase maps in Figs. 8-10 are color-coded without confidence intervals, so it is unclear whether the apparent enlargement is robust to initial conditions, finite simulation length, or noise realizations. Since this claim is prominent in the abstract and in the final summary of findings, it should be supported by a quantitative measure, such as the area of each regime in parameter space as a function of Xi, with error bars computed from repeated simulations or bootstrapping.
minor comments (5)
  1. [Sec. II.B] The text says 'only fast-spiking inhibitory neurons ( only-FS network). or only low-threshold spiking inhibitory neurons ( only-FS network )'; the second instance should read 'only-LTS network'.
  2. [Sec. III.D and Fig. 11 caption] Fig. 11 refers to 'the parameter controlling the excitatory heterogeneity Xi', but Xi controls the inhibitory heterogeneity, not the excitatory one. The same mislabeling appears in the text immediately above Fig. 11.
  3. [Fig. 10 caption] The caption begins 'The man time delay τ as a function of Xi' and should be 'The mean time delay'.
  4. [General] No code or data availability statement is provided, and the simulation details (number of realizations, simulation length for each point, random seed handling) are not fully specified, which would be needed for independent reproduction of the parameter maps.
  5. [Sec. I] The introduction contains an incomplete citation '[6, 12? ]'; the placeholder should be resolved.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the phase-diversity and DS-AS route results are self-contained simulation findings, and the Sec. III.D period-ratio mechanism is an explicitly tentative, falsifiable suggestion rather than a fitted prediction.

full rationale

The paper does not fit any parameter to reproduce a target time delay or phase regime; all phase-diversity observations (DS, AS, ZL, BI) are direct simulation outputs of the coupled Izhikevich network. The inhibitory-heterogeneity parameter Xi is defined by Eqs. (6)-(7) independently of the measured phase relations, and the claimed enlargement of bistability/zero-lag regions is a visual comparison of phase diagrams, not an algebraic identity. The only candidate for a circular step is the proposed mechanism in Sec. III.D, where the authors compare the uncoupled free-running periods (gE = 0) with the coupled transition route and 'suggest' that bistability is facilitated if TR < TS already in the DS regime, while zero-lag transitions occur when TR = TS. This is not circular in the prohibited sense: the periods are computed from an independent uncoupled simulation, no parameter is fitted to force the correlation, and the authors explicitly acknowledge the limitation that 'Regarding only the periods, it is not possible to predict if the system will be in DS or AS when coupled' and that 'a complete mechanism explaining the transition... remains to be discovered.' The self-citations to Refs. [48,52,53] are contextual or methodological (e.g., using the excitatory-heterogeneity parameterization from Ref. [53]) and are not load-bearing for the novel inhibitory-heterogeneity claims. No uniqueness theorem or ansatz is smuggled in via self-citation. The derivation chain is therefore self-contained, and any weakness in the Sec. III.D mechanism is a concern about post-hoc explanatory strength, not circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central modeling result depends on several hand-chosen parameters (Xi, X, gI, gE, R) and on domain assumptions about how well Izhikevich populations represent cortical circuits. No new physical entities are introduced. The paper does not claim to derive the phase regimes from first principles; it documents simulation observations and a suggested period-ratio mechanism.

free parameters (5)
  • Xi (inhibitory heterogeneity) = varied from -0.045 to 0.045
    Controls the fraction of FS versus LTS inhibitory neurons in the receiver; central control variable, not fitted to experimental data.
  • X (excitatory heterogeneity) = varied from -5 to 10
    Controls the distribution of excitatory neuron types, following Ref. [53]; scanned to map phase regimes.
  • gI (receiver inhibitory conductance) = examples 4.0, 5.0, 6.0 nS
    Receiver inhibitory synaptic strength that shapes the feedback controlling AS; varied by hand.
  • gE (sender-receiver coupling) = 0.5 nS in coupled runs, 0 in uncoupled runs
    Strength of excitatory synapses from sender to receiver; fixed at 0.5 nS except for the uncoupled comparison.
  • R (external Poisson input rate) = 2400 Hz
    Sets the main oscillation frequency of the population activity; fixed by hand, not fitted.
assumptions (4)
  • domain assumption Euler integration with time step 0.05 ms accurately reproduces the Izhikevich network dynamics.
    The full model is integrated with a fixed-step Euler scheme (Sec. II.C); no convergence test or comparison with stiff solvers is provided.
  • domain assumption A population of 400 excitatory and 100 inhibitory Izhikevich neurons with 10% random connectivity represents cortical-like circuits.
    Motivated by neocortical 80/20 ratio and previous studies (Sec. II.A), but no biological validation is presented.
  • domain assumption The smoothed mean membrane potential Vx and its detected peaks faithfully represent each population's oscillation and phase relation.
    All phase delays tau_i are computed from peak times of the average membrane potential after sliding-window smoothing (Sec. III.A).
  • domain assumption FS and LTS Izhikevich parameter values capture the functionally relevant inhibitory neuron variability.
    The paper varies only a and b for inhibitory neurons, keeping c and d fixed; this reduced parameterization is assumed sufficient for the phase-relation phenomena.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The role of inhibitory neuronal variability in modulating phase diversity between coupled networks." pith.science (2026). https://pith.science/paper/N2QHKH4F

@misc{pith2026241119664,
  author       = {Pith},
  title        = {Pith review of: The role of inhibitory neuronal variability in modulating phase diversity between coupled networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N2QHKH4F}},
  note         = {Machine review of arXiv:2411.19664}
}
read the original abstract

Neuronal heterogeneity, characterized by the presence of a multitude of spiking neuronal patterns, is a widespread phenomenon throughout the nervous system. In particular, the brain exhibits strong variability among inhibitory neurons. Despite the huge neuronal heterogeneity across brain regions, which in principle could decrease synchronization, cortical areas coherently oscillate during various cognitive tasks. Therefore, the functional significance of neuronal heterogeneity remains a subject of active investigation. Previous studies typically focus on the role of heterogeneity in the dynamic properties of only one population. Here, we explore how different types of inhibitory neurons can contribute to the diversity of the phase relations between two cortical areas. This research sheds light on the potential impact of local properties, such as neuronal variability, on communication between distant brain regions. We show that both homogeneous and heterogeneous inhibitory networks can exhibit phase diversity and nonintuitive regimes such as anticipated synchronization (AS) and phase bistability. It has been proposed that the bi-stable phase could be related to bi-stable perception, such as in the Necker cube. Moreover, we show that heterogeneity enlarges the region of zero-lag synchronization and bistability. We also show that the parameter controlling inhibitory heterogeneity modulates the transition from the usual delayed synchronization regime (DS) to AS. Finally, we show that the inhibitory heterogeneity drives the internal dynamics of the free-running population. Therefore, we suggest a possible mechanism to explain when the DS-AS transition occurs via zero-lag synchronization or bi-stability.

Figures

Figures reproduced from arXiv: 2411.19664 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic representation of two unidirectionally [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Examples of neuronal time series illustrate the [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Characterizing the parameters controlling neuronal [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Revealing phase relations diversity in our motifs. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Comparison between the two different transitions [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Phase diversity is modulated by both inhibitory [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Scanning parameter space to visualize the phase re [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10. (a)-(d) The man time delay [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Comparing the free-running period of the re [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

68 extracted references · 68 canonical work pages

  1. [1]

    Singer, Neuron Review 24, 49 (1999)

    W. Singer, Neuron Review 24, 49 (1999)

    work page 1999

  2. [2]

    Fries, Trends in Cognitive Sciences 9, 474 (2005)

    P. Fries, Trends in Cognitive Sciences 9, 474 (2005)

    work page 2005

  3. [3]

    A. M. Bastos, J. Vezoli, and P. Fries, Current Opinion in Neurobiology 31, 173 (2015)

    work page 2015

  4. [4]

    Maris, T

    E. Maris, T. Womelsdorf, R. Desimone, and P. Fries, Neuroimage 74, 99 (2013)

    work page 2013

  5. [5]

    Maris, P

    E. Maris, P. Fries, and F. van Ede, Trends in Neuro- sciences (2016). 11

    work page 2016

  6. [6]

    Di Volo and A

    M. Di Volo and A. Destexhe, Scientific reports 11, 17611 (2021)

    work page 2021

  7. [7]

    Angelo, E

    K. Angelo, E. A. Rancz, D. Pimentel, C. Hundahl, J. Hannibal, A. Fleischmann, B. Pichler, and T. W. Margrie, Nature 488, 375 (2012)

    work page 2012

  8. [8]

    Beaulieu, Brain research 609, 284 (1993)

    C. Beaulieu, Brain research 609, 284 (1993)

    work page 1993

Show all 68 references
  1. [9]

    Markram, M

    H. Markram, M. Toledo-Rodriguez, Y. Wang, A. Gupta, G. Silberberg, and C. Wu, Nature reviews neuroscience 5, 793 (2004)

    2004

  2. [10]

    Borges, P

    F. Borges, P. Protachevicz, R. Pena, E. Lameu, G. Higa, A. Kihara, F. Matias, C. Antonopoulos, R. de Pasquale, A. Roque, et al. , Physica A: Statistical Mechanics and its Applications 537, 122671 (2020)

    2020

  3. [11]

    M. P. Nawrot, C. Boucsein, V. R. Molina, A. Riehle, A. Aertsen, and S. Rotter, Journal of neuroscience meth- ods 169, 374 (2008)

    2008

  4. [12]

    K. L. Rossi, R. C. Budzisnki, J. A. P. Silveira, B. R. R. Boaretto, T. L. Prado, S. R. Lopes, and U. Feudel, arXiv preprint arXiv:2003.03289 (2020)

    2020 arXiv

  5. [13]

    A. N. Burkitt, Biological cybernetics 95, 1 (2006)

    2006

  6. [14]

    Borges, P

    F. Borges, P. Protachevicz, V. Santos, M. Santos, E. Gabrick, K. Iarosz, E. Lameu, M. Baptista, I. Cal- das, and A. Batista, in Indian Acad Sci Conf Ser , Vol. 3 (2020) pp. 97–103

    2020

  7. [15]

    S. J. Tripathy, K. Padmanabhan, R. C. Gerkin, and N. N. Urban, Proceedings of the National Academy of Sciences 110, 8248 (2013)

    2013

  8. [16]

    Golomb and J

    D. Golomb and J. Rinzel, Physical review E 48, 4810 (1993)

    1993

  9. [17]

    Shamir and H

    M. Shamir and H. Sompolinsky, Neural computation 18, 1951 (2006)

    2006

  10. [18]

    P´ erez, C

    T. P´ erez, C. R. Mirasso, R. Toral, and J. D. Gunton, Philosophical Transactions of the Royal Society A: Math- ematical, Physical and Engineering Sciences 368, 5619 (2010)

    2010

  11. [19]

    Mejias and A

    J. Mejias and A. Longtin, Physical Review Letters 108, 228102 (2012)

    2012

  12. [20]

    J. F. Mejias and A. Longtin, Frontiers in computational neuroscience 8, 107 (2014)

    2014

  13. [21]

    Renart, P

    A. Renart, P. Song, and X.-J. Wang, Neuron 38, 473 (2003)

    2003

  14. [22]

    J. Hass, S. Ardid, J. Sherfey, and N. Kopell, bioRxiv , 645663 (2019)

    2019

  15. [23]

    Model, J Neurophysiol 89, 2707 (2003)

    N. Model, J Neurophysiol 89, 2707 (2003)

    2003

  16. [24]

    Marsat and L

    G. Marsat and L. Maler, Journal of neurophysiology 104, 2543 (2010)

    2010

  17. [25]

    Padmanabhan and N

    K. Padmanabhan and N. N. Urban, Nature neuroscience 13, 1276 (2010)

    2010

  18. [26]

    Savard, R

    M. Savard, R. Krahe, and M. Chacron, Neuroscience 172, 270 (2011)

    2011

  19. [27]

    H. U. Voss, Phys. Rev. E 61, 5115 (2000)

    2000

  20. [28]

    H. U. Voss, Phys. Rev. E 64, 039904 (2001)

    2001

  21. [29]

    H. U. Voss, Phys. Rev. Lett. 87, 014102 (2001)

    2001

  22. [30]

    Ciszak, O

    M. Ciszak, O. Calvo, C. Masoller, C. R. Mirasso, and R. Toral, Phys. Rev. Lett. 90, 204102 (2003)

    2003

  23. [31]

    Masoller and D

    C. Masoller and D. H. Zanette, Physica A 300, 359 (2001)

    2001

  24. [32]

    Hern´ andez-Garc ´ ıa, C

    E. Hern´ andez-Garc ´ ıa, C. Masoller, and C. Mirasso, Phys. Lett. A 295, 39 (2002)

    2002

  25. [33]

    Sausedo-Solorio and A

    J. Sausedo-Solorio and A. Pisarchik, Physics Letters A 378, 2108 (2014)

    2014

  26. [34]

    Sivaprakasam, E

    S. Sivaprakasam, E. M. Shahverdiev, P. S. Spencer, and K. A. Shore, Phys. Rev. Lett. 87, 154101 (2001)

    2001

  27. [35]

    Ciszak, C

    M. Ciszak, C. R. Mirasso, R. Toral, and O. Calvo, Phys. Rev. E 79, 046203 (2009)

    2009

  28. [36]

    Tang and J

    S. Tang and J. M. Liu, Phys. Rev. Lett. 90, 194101 (2003)

    2003

  29. [37]

    Kostur, P

    M. Kostur, P. H¨ anggi, P. Talkner, and J. L. Mateos, Phys. Rev. E 72, 036210 (2005)

    2005

  30. [38]

    Pyragien` e and K

    T. Pyragien` e and K. Pyragas, Nonlinear Dynamics 74, 297 (2013)

    2013

  31. [39]

    A. Y. Simonov, S. Y. Gordleeva, A. Pisarchik, and V. Kazantsev, JETP Letters 98, 632 (2014)

    2014

  32. [40]

    Hayashi, S

    Y. Hayashi, S. J. Nasuto, and H. Eberle, Physical Review E 93, 052229 (2016)

    2016

  33. [41]

    G. C. Dima, M. Copelli, and G. B. Mindlin, International Journal of Bifurcation and Chaos 28, 1830025 (2018)

    2018

  34. [42]

    M. A. Pinto, O. A. Rosso, and F. S. Matias, Physical Review E 99, 062411 (2019)

    2019

  35. [43]

    Dalla Porta, F

    L. Dalla Porta, F. S. Matias, A. J. dos Santos, A. Alonso, P. V. Carelli, M. Copelli, and C. R. Mirasso, Frontiers in Systems Neuroscience 13 (2019)

    2019

  36. [44]

    F. S. Matias, P. V. Carelli, C. R. Mirasso, and M. Copelli, Phys. Rev. E 84, 021922 (2011)

    2011

  37. [45]

    F. S. Matias, L. L. Gollo, P. V. Carelli, C. R. Mirasso, and M. Copelli, Phys. Rev. E 94, 042411 (2016)

    2016

  38. [46]

    F. S. Matias, P. V. Carelli, C. R. Mirasso, and M. Copelli, Physical Review E 95, 052410 (2017)

    2017

  39. [47]

    C. R. Mirasso, P. V. Carelli, T. Pereira, F. S. Matias, and M. Copelli, Chaos: An Interdisciplinary Journal of Nonlinear Science 27, 114305 (2017)

    2017

  40. [48]

    F. S. Matias, L. L. Gollo, P. V. Carelli, S. L. Bressler, M. Copelli, and C. R. Mirasso, NeuroImage 99, 411 (2014)

    2014

  41. [49]

    F.-L. P. Carlos, M.-M. Ubirakitan, M. C. A. Rodrigues, M. Aguilar-Domingo, E. Herrera-Guti´ errez, J. G´ omez- Amor, M. Copelli, P. V. Carelli, and F. S. Matias, Phys- ical Review E 102, 032216 (2020)

    2020

  42. [50]

    Brovelli, M

    A. Brovelli, M. Ding, A. Ledberg, Y. Chen, R. Nakamura, and S. L. Bressler, Proc. Natl. Acad. Sci. USA 101, 9849 (2004)

    2004

  43. [51]

    R. F. Salazar, N. M. Dotson, S. L. Bressler, and C. M. Gray, Science 338, 1097 (2012)

    2012

  44. [52]

    J. N. Machado and F. S. Matias, Physical Review E 102, 032412 (2020)

    2020

  45. [53]

    K. V. Brito and F. S. Matias, Physical Review E 103, 032415 (2021)

    2021

  46. [54]

    K¨ osem, A

    A. K¨ osem, A. Basirat, L. Azizi, and V. Van Wassenhove, Journal of neurophysiology 116, 2497 (2016)

    2016

  47. [55]

    E. M. Izhikevich, Int. J. Bifurcat. Chaos 10, 1171 (2000)

    2000

  48. [56]

    Izhikevich, IEEE Transaction on Neural Networks 14, 1569 (2003)

    E. Izhikevich, IEEE Transaction on Neural Networks 14, 1569 (2003)

    2003

  49. [57]

    Izhikevich, J

    E. Izhikevich, J. Gally, and G. Edelman, Cerebral Cortex 14, 933 (2004)

    2004

  50. [58]

    F. S. Matias, P. V. Carelli, C. R. Mirasso, and M. Copelli, PloS one 10, e0140504 (2015)

    2015

  51. [59]

    R. Gast, S. A. Solla, and A. Kennedy, Proceedings of the National Academy of Sciences 121, e2311885121 (2024)

    2024

  52. [60]

    G. A. Orban, K. Hoffmann, and J. Duysens, Journal of Neurophysiology 54, 1026 (1985)

    1985

  53. [61]

    Nowak, M

    L. Nowak, M. Munk, P. Girard, and J. Bullier, Visual neuroscience 12, 371 (1995)

    1995

  54. [62]

    Kerzel and K

    D. Kerzel and K. R. Gegenfurtner, Current Biology 13, 1975 (2003)

    2003

  55. [63]

    Jancke, W

    D. Jancke, W. Erlhagen, G. Sch¨ oner, and H. R. Dinse, The Journal of physiology 556, 971 (2004)

    2004

  56. [64]

    G. D. Puccini, M. V. Sanchez-Vives, and A. Compte, PLoS computational biology 3, e82 (2007). 12

    2007

  57. [65]

    L. M. Martinez, M. Molano-Mazo, X. Wang, F. T. Som- mer, and J. Hirsch, Neuron 81, 943 (2014)

    2014

  58. [66]

    Rospars, A

    J.-P. Rospars, A. Gr´ emiaux, D. Jarriault, A. Chaffiol, C. Monsempes, N. Deisig, S. Anton, P. Lucas, and D. Martinez, PLoS Computational Biology 10, e1003975 (2014)

    2014

  59. [67]

    Stepp and M

    N. Stepp and M. T. Turvey, Cognitive Systems Research 11, 148 (2010)

    2010

  60. [68]

    Stepp and M

    N. Stepp and M. T. Turvey, Journal of Experimental Psy- chology: Human Perception and Performance 43, 914 (2017)

    2017

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.