Dear Dr. Duque-Daza,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Both reviewers find the modeling framework potentially valuable, but Reviewer 1 raises major concerns that must be addressed for acceptance, particularly regarding: (i) the explicit and consistent mapping to the valence–arousal circumplex, (ii) conceptual constraints and interpretability of the model variables (e.g., non-negativity of emotional intensity), (iii) specification and justification of coupling matrices, and (iv) numerical methods, convergence, and reproducibility. These points are required revisions to ensure technical soundness and reproducibility. Reviewer 2’s comments mainly concern clarifications, writing quality, and data/code availability, which should also be addressed.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Partly

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: N/A

Reviewer #2: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: No

Reviewer #2: No

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4. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: No

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Reviewer #1: This manuscript proposes a dynamic system model of emotional contagion based on Russell's circumplex model of affect. The affective state of each agent is represented as a complex phasor zi(t), where the radius ri(t) represents the emotional intensity and the angle θi(t) represents the affective orientation in the valence-arousal space. The model combines (i) a radial, damped, driven oscillator with linear diffusive coupling and (ii) an angular, pendulum-like oscillator with sinusoidal coupling, which is solved numerically (RK4 / RKF45) and demonstrated using several network scenarios.

The modeling direction is potentially interesting and could be useful as a generative/simulation framework. However, in its current form, the manuscript has several fundamental problems that prevent an assessment of its scientific soundness and reproducibility, particularly with regard to mapping to circumplex variables, the interpretability of parameters, the construction and scaling of coupling matrices, and numerical verification. The conclusions also overstate the biological basis and predictability compared to what is shown.

1) Mapping to valence/ arousal is not explicitly defined and the psychological interpretation is unclear.

- The manuscript states that θ "corresponds to the configuration of valence and arousal", but does not provide an explicit, testable mapping between (r,θ) and the standard circumplex axes. Readers will expect something like valence = r cos θ, arousal = r sin θ. Please define this mapping and keep it consistent across figures. Also define "neutrality" precisely (what is r = 0 in psychological/ measurement terms?)

2) Radial dynamics allow r <0 which is incompatible with radius as intensity.

Equations (1-2) treat ri(t) as a state variable. Because r is defined as a radial distance, negative values are conceptually problematic. The manuscript would need to give a constrained formulation ensuring ri(t) ≥0 or a clear mathematical argument and empirical demonstration that the chosen parameter regimes prevent r <0. Without addressing this, the core representation z is not well-defined as a circumplex embedding as currently presented.

3) Separation of radial and angular dynamics is assumed but not justified.

As written, ri(t) and θi(t) evolve independently and are only recombined at the end to form zi(t). In affective science, intensity and direction can interact (high arousal affecting valence dynamics or vice versa). Please justify why separability is appropriate for emotional contagion, or consider adding cross-terms and/ or discussing limitations more explicitly.

4) Novelty/ positioning

The introduction overstates novelty by implying prior work is mainly categorical or static propagation. Please add a stronger related-work section that identifies the closest mathematical relatives and state clearly what is new here.

5) Coupling matrices Kr, Kθ

Key properties are underspecified: directed vs undirected, allowed sign (negative?), normalization/ bounds, static vs time varying and how K is chosen per scenario. The Appendix uses very large couplings (e.g. 50/500) and includes a nonzero diagonal term, which needs explanation. These details are required for interpretability and reproducibility.

6) Table 1 emotion coordinates

Table 1 provides polar coordinates used as initial conditions but does not justify their provenance or derivation. Please cite a dataset/ method or clearly label values as illustrative.

7) Numerical methods

The numerical methods section is currently underspecified and contains potentially misleading statements. Classical RK4 is a fixed-step method, yet the text mentions “fixed or adaptive step size,” without reporting actual step sizes or adaptive tolerances used for each figure. In addition, the manuscript suggests RKF45 is advantageous for stiff regimes; however, explicit RK methods are generally not reliable for stiffness and may require prohibitively small steps. Please report full solver settings (Δt or tolerances, simulation horizon, angle wrapping conventions) and include a convergence/robustness analysis (e.g., step-halving or tolerance tightening). The Appendix currently shows outcomes can change markedly with “numerical accuracy”; define what was varied and demonstrate convergence, and separate true dynamical sensitivity from numerical artifacts.

8) Conclusions and metrics

Conclusions appear overstated (biological grounding, "predictive reliability") relative to evidence; please moderate language or add validation. At present, the work is best framed as an exploratory computational framework rather than an empirically validated predictive model. Define quantitative outcome metrics for synchronization, convergence/ divergence, "dragging/ resonance" and any claims of chaos.

9) Presentation and english (minor/ editorial)

The manuscript is generally understandable, but it would benefit from editing the conciseness and precision. Please correct specific issues including typographical errors and duplicated paragraphs in the Appendix around Figure 16.

10) Data/ code availability

Because the findings are simulation-based, full reproducibility requires public access to the code (or complete pseudocode sufficient for reimplementation), all parameter files and initial conditions (including Table 1 values and the coupling matrices used in each scenario), and scripts or raw outputs needed to reproduce figures end-to-end. If these materials are not yet provided in a public repository, I strongly encourage the authors to deposit them and reference them in the Data Availability Statement.

Summary

I believe the modeling idea could be valuable, but major revisions are needed to (i) clearly define the circumplex mapping, (ii) address conceptual constraints such as r ≥ 0, (iii) specify and justify coupling construction/scaling, and (iv) provide rigorous numerical verification and reproducible computational details. Only after these points are addressed can the technical soundness and the strength of the conclusions be adequately evaluated.

Reviewer #2: This manuscript proposes a novel approach for modeling the temporal evolution of affective dynamics during emotional contagion. The authors describe an individual’s emotional state using two independent oscillators, representing emotional intensity and orientation within Russell’s circumplex plane. The study aims to provide the scientific community with a more accurate yet computationally efficient framework to simulate affective dynamics emerging in complex social settings.

While the topic is of interest, the manuscript requires minor revisions concerning the data availability and writing quality. Specifically, in contrast with PLOS One Data policy, the authors do not provide full access to data which are available "upon request" via email. This approach does not meet the journal’s requirements therefore should be revised. Concerning the writing, I found some typographical errors, for instance:

Line 89 : "yhe" instead of "the";

Line 268 : "We" is capitalized incorrectly in the middle of the sentence;

I suggest reading carefully the entire manuscript to identify and correct additional typographical or stylistic issues.

Shifting to methodological aspects, the model in general is intuitive and appropriate for describing affective dynamics as it comprises both internal and external emotional influences. Still, some aspects need further clarification.

Firstly, the elements appearing in Equations (2) and (4) are described in a chaotic and fragmented manner (lines within the range 105–132), especially the term corresponding to emotional contagion. I suggest following the order in which these elements appear in the equations and giving them a complete characterization, all at once. This refers to both mathematical explanation and social interpretation.

Regarding the mathematical framework, to fully understand how the model works, further mathematical contextualization may be useful, especially if the paper is addressed to a non-experts audience such as psychologists. Therefore, it would be helpful to explain what the role of the elastic and damping forces in an oscillator is, and how these translate into the context of affective regulation.

For instance, the concept of internal “inertia” to affective changes, modeled by the elastic force, is very appealing but lacks a proper explanation. Indeed, the model description does not include the term ri-ri*. This aspect should be given greater consideration as it is important for emotional regulation just like external influences. Furthermore, the use of the spring metaphor to illustrate resistance to affective changes is well-chosen and could help make the model even more accessible if accompanied by a clear explanation.

Moreover, the role of the external force τi(t) is not clear: What does It represent in a social setting? Simulations miss initializing this variable and explaining its role, as well. Without real-life examples, it is even harder to understand what this emotional source might represent.

Overall, this paper addresses an interesting and relevant topic, providing simulations of highly diverse social contexts and offering valuable insights for the study of emotional contagion. For future research, the authors may consider extending the application of the model to real-world settings, using either a priori or real-time measures of emotional influences among individuals, which would enable predictions of the dynamics of emotional states in everyday social interactions.

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what does this mean?). If published, this will include your full peer review and any attached files.

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Reviewer #1: Yes: Stella Wienhold

Reviewer #2: No

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A Dynamical Systems Model of Emotional Contagion: Oscillatory Coupling in the Circumplex of Affect

PONE-D-25-53517R1

Dear Dr. Duque-Daza,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Alberto Greco

Academic Editor

PLOS One

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #2: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #2: (No Response)

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3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #2: (No Response)

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4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #2: (No Response)

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5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #2: (No Response)

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Reviewer #2: (No Response)

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what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review?  For information about this choice, including consent withdrawal, please see our Privacy Policy

Reviewer #2: No

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