PONE-D-20-37260

A THEORETICAL ANALYSIS OF COMPLEX ARMED CONFLICTS

PLOS ONE

Dear Dr. Della Rossa,

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 indicate some positive points but also both of them remark that the article needs to be carefully rewritten as there are a lot of points to be studied with care. Mainly these problems were with the claims with the relationship to real-world examples.

Please submit your revised manuscript by Mar 25 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

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We look forward to receiving your revised manuscript.

Kind regards,

Roberto Barrio

Academic Editor

PLOS ONE

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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?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Partly

**********

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

Reviewer #1: N/A

Reviewer #2: N/A

**********

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

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No

Reviewer #2: Yes

**********

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

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: No

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Dear Editor,

I have reviewed the manuscript entitled “A theoretical analysis of complex armed conflicts.”

In the paper, the authors propose an idealized dynamical model for conflicts involving multiple group-level actors. They model natural growth, recruitment, and attrition from interaction along with a natural characteristic size to which actors tend in the absence of interaction. They then consider interactions between two types of actors that they distinguish as being either “defensive” or “attack” types in detail for N=2 and N=3. For such analysis, they rely on standard dynamical systems analysis, identifying various fixed points of the system, stable periodic orbits, chaos, and sensitivity to initial conditions. They discuss N>3 as well as various other considerations that might be relevant for armed conflict. They relate aspects of the dynamical system with historical examples of conflict that are evocative of their findings throughout the text.

Overall, I found the model they they wrote down to be interesting with a rich variety of behaviors and that the authors were detailed and methodical in their exploration of the model. This is an interesting extension of the class of models specified by Lanchester. Furthermore, they consider a number of important variation of the model. Finally, the historical allusions were interesting to read in the context of the model (even if they also presented some problems).

As a scientific note, I would ask the authors to address, if briefly, the role of spatial dynamics and noise on conflict dynamics.

Despite these positive comments, there were major issues with the manuscript besides the mathematical model. These problems were with the strong claims made about the relationship to real-world examples, addressing the relevant literature, many grammatical issues, unclear and figures. Though I believe these issues could be fixed, they require substantial manuscript revision. With these shortcomings, I cannot recommend the manuscript for publication at this time.

Please see below for more details.

I would strongly recommend that the authors ask an English-speaking colleague to look over their manuscript. Here, is a non-exhaustive list of some grammatical errors.

In the abstract, “compensating for suffered” and “they inflict onto their enemies.”

Line 35, “defensive” not “defense”

Lines 45-48, run-on sentence

Line 31 non-stationary

There are many such typos that need to be fixed as well as other syntatical issues throughout the text.

Though the historical allusions are nice, the authors are quite strong in their language about the similarity of their model results. For example, lines 221-223 make a general claim about(a) historical conflicts being stalemates and (b) being explained by their model (“This explains why many conflicts…”) The qualitative examples are only an allusion as presented in the text and therefore do not justify such a strong claim. Similar claims are repeated throughout the text. Indeed, the authors emphasized the ideal assumptions made in their model at parts of the paper but were assertive in their claims at other parts, disjunction that should be reconciled.

The authors do not engage with the literature sufficiently. For example, the authors dismiss “traditional descriptive conceptual models,” at the beginning as a contrast to their work. This is an overly general and unspecific claim. Indeed, Richardson did propose a dynamical model (even if it was horribly wrong). Furthermore, such a strong claim warrants much more than two citations—especially if these are “traditional” models then there should be a large literature to cite.

In the discussion, the authors refer to statistical analysis of conflict. Again, there is much literature on statistical analysis of conflict going beyond Clauset and Gleditsch. A sparse sample of examples is

Cederman, L.-E. Modeling the Size of Wars: From Billiard Balls to Sandpiles. APSR 97, 135–150 (2003).

Johnson, N. F. et al. Simple mathematical law benchmarks human confrontations. Sci. Rep. 3, 3463 (2013).

Lee, E. D., Daniels, B. C., Myers, C. R., Krakauer, D. C. & Flack, J. C. Scaling theory of armed-conflict avalanches. Phys. Rev. E 102, 042312 (2020).

Picoli, S., Castillo-Mussot, M. del, Ribeiro, H. V., Lenzi, E. K. & Mendes, R. S. Universal bursty behaviour in human violent conflicts. Sci. Rep. 4, 4773 (2015).

Roberts, D. C. & Turcotte, D. L. Fractality and Self-Organized Criticality of Wars. Fractals 6, 351–357 (1998).

Zammit-Mangion, A., Dewar, M., Kadirkamanathan, V. & Sanguinetti, G. Point process modelling of the Afghan War Diary. Proc. Natl. Acad. Sci. 109, 12414–12419 (2012).

Beyond these examples, the authors do not cite some classic examples of dynamical systems approaches including Lanchester’s work on dynamical models of conflict.

There are classic papers on dynamical systems analysis including chaotic attractors besides Strogatz’s text.

Many of the figures seem unnecessary. Furthermore, some of them are missing labels and legends such Figure 19.

Miscellaneous question:

What happen to the critical points as parameters are changed?

Reviewer #2: This manuscript considers a model for the size of an army, and provides an analysis for a number of cases. It also tries to interpret the dynamical systems analysis using historical examples.

I have two major concerns regarding this text.

First, I have troubles with how the model is presented. Only gradually did I conclude that the army size is main variable. It is stated at lines 80-81, but to understand the introduction a reader needs this earlier. And then finally in the conclusion they present the assumptions as conjectures (lines 631-44). The authors have worked on this topic before, but as a newbie I had a hard time following what it was about. This part should be rewritten so that a math modeller can follow from the start, i.e. assumptions, main variables. It is partially there, but it is scattered. A non-exhaustive list of suggestions:

-l29 Stalemate; would you care to define this? As in population biology, this concerns a attractor with positive state variables I figure?

-l30 "in the sizes and in the losses"; at this point entirely unclear.

-l36 at this point it is unclear what "their recruitment" means. It would not hurt either to explicitly present the 2D ODE system for both D-D and A-D groups. And then show how we see this difference in recruitment. At the end, I still had no idea, and it should be clear from the manuscript, not from work from my side.

-l135,l168; This part on bureaucracy I cannot follow.

-During a stalemate, you would not fight as the fight is fair and you would not gain anything. Yet, the losses in your model are not zero. Please motivate this.

Second, I find the historical reasoning to be too anecdotal. I know modelling and dynamical systems, but am not a history expert. I have checked some statements with an expert on warfare. I would add that at least one such person with historical warfare expertise should be reviewing too. I strongly suggest to make a split in the presentation here. For example, for D-D conflicts, present the bifurcation and its general interpretion, and then with a separate heading discuss historical examples, and then with more argumentation why it fits. Now math and history mingle in a suboptimal manner.

Some considerations

l189 post-Westphalian period, please be more specific. Do you mean the year 1648? But it means more than just that!

l224-227; Caution should be added to this interpretation of the Sparta-Athena war.

l230-1; the use of tanks... Germans used tanks too although late, and had antitank ammunition. You point at a single battle only, so why was that crucial only in 1918, while the first tanks were introduced in September 1916? The Americans joining the battle is irrelevant here? Or the lowered support of the German population?

l233 The Enigma code was crucial for the sea, I agree. But it is a long stretch to reduce this to a perturbation, this would rather be a change in parameter values (higher attack/defense efficiency), i.e. property ii. Move it there, and explain it better.

l290-293; This is not too specific. UK and France started war in 1939, when Poland was invaded and the French had the Maginot-line. The Blitzkrieg through the Benelux to avoid it and get to Dunkurque is not readily captured by your model.

l320 Here too, suddenly in brackets some history is dropped. Now I am from Europe, and after a wrinkle I read on, but what about readers from other parts of the world? Please rewrite it properly, dissecting math from history.

l372-375; This is what we would say from a Western perspective, but I am inclined to say we do not that their willingness decreased. That population did not have much voice nor choice. For the US it was a foreign war, for the VietCong a civil war. It might be wise to expand your description, again.

l454-455; "as observed in many real conflicts." I do not like it that you just state it somewhere in passing. This deserves proper data.

l676-9 I do not follow your arguments on the Yugoslavian war.

Minor issues and typo's:

l27; the following reads nicer "for a review see MacKay (2015))"

l31; are contingent --> depend

l31; non-stationary (with hyphen) (line 523 too, I just stopped noting them)

l92; , after large

l115; close to one (unit is awkward)

l156; space before is

l164; that THE parameter k_i

l185; "no details are given"...; be constructive, just say you use this software, and btw, the reference is inadequate as the 2003 version does not support connecting orbit detection. The MCMDS(2008)-paper seems more appropriate.

l187; "are hidden, but avaialable" is not so nice for an open access paper. Just say "are all listed in".

l192-4; "fixed at will": I am lost! I think you fix all other parameters, and vary b_1 and c_2. Or even better, "their influence on the dynamics is explored systematically."

l211 "surrounding"; a bifurcation diagram either includes the phase portraits so that "surrounding" is superfluous OR the caption of Figure 3 is incomplete as it then mentions only one part of the figure.

l211 pointed out --> illustrated

l215/6 I wonder whether "are highly sensitive" is adequate. Surely "depend" would fit, but it depends what measure one uses to say it depends a lot.

l256 dimension -> size

l258 I wonder what "characteristic" means in this context.

l268 Westerlands's

l326-7; sentence is not wrong, just hard to read.

l351 encapsulated -> summarized

l363 more rare? If I look at figure 10, I would argue the opposite, the mean loss has a plateau at high values and only temporarily drops.

l382 add both after they

l401 please rephrase, difficult to parse

l419-30; can you squeeze this digression?

l442; other conflict types (instead of types of conflict) for readability.

Figure 14; consider using L_i^k and L_i^{k+1} instead of using * and **

l448 add an before aperiodic

l450 a superscript is missing, either * or k

l464 add "the years" before 2013

l469 delete last "of"

l470 add maximal before Lyapunov

l499 "achieve breakthroughs in stalemates", not interrupt, that would mean stop fighting, always a better idea.

l526 strange dots

l548 Why does your signal w(t) need to follow an ODE? as you want to compute these LE's too? Please specify.

l581 pure (it's an adjective)

l605 analysis do confirm --> analyses confirm

l619 Replace the = sign by something more appropriate.

l634 State should be put in " as otherwise it does not apply to guerrilla groups

l634 please clarify "that interprets the overall"

l637 defensive

l642 delete (losses)

l648 "not as crude" seems entirely out of place.

l677 I object to "solved", that is not a neutral term here.

l678 part to --> part in?

Appendix 5; I object to the adjective military and environmental for LE's. There are two issues, much as before I suggest to distinguish between math and context. Intrinsic and forced LE's, seem clearer from an analysis point of view.

btw. I looked the ref given in line 839-40, but then it would help if say you're using the "method based on qr-decomposition", if that's what you are using.

l868; clarify "simply replicate"

l935-6; I do not think that periods getting closer has to do with synchrony. The differnce between 1 and 15 weeks is still large. I tried to read it a couple of times, but I get confused as T_cycle=52weeks implies synchrony to me if T_env=1 year.

l965; remove alive

l1109; inconsistent initials with dots

ll141; a journal for an arxiv-preprint ?!?

On the one hand it is an attractive idea to describe just the size of an army over time. On the other hand, the interpretation should be done with much more care. There is much to change in this text, but it might be feasible.

**********

6. PLOS authors have the option to publish the peer review history of their article (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.

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Reviewer #1: No

Reviewer #2: No

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PONE-D-20-37260R1A THEORETICAL ANALYSIS OF COMPLEX ARMED CONFLICTSPLOS ONE

Dear Dr. Della Rossa,

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.

Please submit your revised manuscript by Nov 14 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Roberto Barrio

Academic Editor

PLOS ONE

Journal Requirements:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

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

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

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

Reviewer #1: Yes

Reviewer #2: N/A

**********

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

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

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

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Dear Editor,

I have read the revised manuscript submitted by Rinaldi et al. I appreciate the work the authors have put into revising the manuscript, and I find it much improved.

One of my main concerns previously was that the connection between the mathematical results and the historical examples were too tenuous for the strength of the claims made in the paper. I find that the new presentation is much better and highlights the big picture without overly specific claims.

Given that neither the other reviewer nor I are historical experts, however, it seems important to verify the historical descriptions with another expert.

Another major concern I had was with the dearth of citations of the extensive literature on conflict modeling. My point was in reference to a balance must be struck with citing widely, relevancy and the length of the manuscript. While I still feel that some additional citations are missing, I trust that this is a result of careful and purposeful selection by the authors.

Finally, I found the grammar and language of the revised manuscript much improved. Thank you for proofreading this with an English speaker. There remain a couple sections where the grammar is unusually strange and many typos remain—namely pages 25 and 33-34.

A few remaining questions and comments

Is there a particular reason for choosing the parameters b1 and c2 for Figure 3 instead, for example, of the ratios of these parameters b1/b2 and c1/c2 for the two models?

In lines 29 and 41 “i.e.” is italicized and then not. I believe it does not need to be italicized, but this should at least be consistent.

There are some sentences with extra spaces like in line 201 amongst other places. This should be an easy find and replace correction.

As the other reviewer mentioned, it is important to justify why the size of the army is the important variable.

Line 73 should be “to the Appendix”

Line 371 do the authors mean “size” and not “dimension”?

Figure 19 typo “raising”

Line 569 “etc.” instead of “…”

Line 569 “the” unnecessary before “experience”

Line 572 no “their” before “damages”

Punctuation issues in lines 573-576

Lines 618-619 Is there more explanation of this “interesting result”?

Line 643 and elsewhere, conflicts are described as “wild”. This sounds rather colloquial to this native English speaker. I would suggest a different word.

Line 750, “terroristic attack” -> “terrorist attack”

Reviewer #2: I see that almost all of my comments addressed satisfactorily, I have two issues remaining:

(a) the text relating to operation Barba Rossa, see below

(b) military LE; I have a suggestion below, and leave the decision to the editor.

I read the version highlighting the changes and found a few typos still, the line numbers refer to that version.

p5 l145; bureaucratic--> bureaucracy

p6 l155 Richardson's models

156-157; models by Lanchester (ref) and Deitchman (reads nicer)

p7 l182 less-> lower

l189 an epidemic (singular), not epidemics (plural)

l218 qualitative --> qualitatively

l261 forces about --> forces were about

l265-6; use of tanks. When you continue with "such innovations" the flow of your story is interrupted, and hard to read. The tanks-part is isolated now. I cannot decide whether you mean both tanks and Stormtroopers or just the latter.

310 Westmorelands' (it is *his* call, yes, I insist)

l341-6 May I suggest to rewrite this? For instance, the state of the Russian army inially was poor even if they had large numbers, and they had chosen a wrong tactic. The mass killing of officers earlier made warfare coordination for the Russians initially hard too. Reading on Barba Rossa, the brutalness came later, and the mass mobilization came later too when German troops had no ammo nor gas left and supplies were hard to get. You may even wonder why the Germans got that far at all. It appears to me that reality here is so complex that your 5-line description is not adequate.

l367 show --> shows

l381 large-N scholarship? I have no clue what you mean. Perhaps you mean large-N studies?

438 objective --> objectives

443-446; Seems an unfinished sentence to me.

502 this rules --> these rules

607 , ... reads as unfinished

808 have --> has

l1215; IBC; with online sources you must state what date you retrieved it.

In the appendix: I still think military LE is a wrong name, and should be avoided. Rather you would like to say this is the intrinsic LE opposed to the environmental LE as it is derived from the "conflict dynamics".

**********

7. PLOS authors have the option to publish the peer review history of their article (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 #1: No

Reviewer #2: Yes: Hil Meijer

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PONE-D-20-37260R2A THEORETICAL ANALYSIS OF COMPLEX ARMED CONFLICTSPLOS ONE

Dear Dr. Della Rossa,

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.

Please submit your revised manuscript by Jan 23 2022 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Roberto Barrio

Academic Editor

PLOS ONE

Journal Requirements:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Additional Editor Comments (if provided):

Dear authors

In this version both reviewers like the article.

There are only very few grammatical remarks that have to be addressed.

Once the few modifications have been done the paper will be in a suitable form to be accepted.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

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

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

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

Reviewer #1: N/A

Reviewer #2: N/A

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

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Reviewer #1: No

Reviewer #2: Yes

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

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Reviewer #1: Yes

Reviewer #2: Yes

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6. Review Comments to the Author

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Reviewer #1: Dear Editor,

I think the manuscript has come a long way, and it is almost ready. I only have a few grammatical comments.

Line numbers refer to the manuscript with the deltas. Brackets indicate my edit.

Lines 151-153: Is there a parenthesis missing? "is unbounded" should be "[are] unbounded"

Line 360: "Many studies confirm[] that"

Figure 21 caption: Is not a more standard way to write "Points A, ..., E" instead "Points A-E"? There is also a period missing at the end.

Line 736: "concerns the idea [of trying] to interrupt"

Line 770: "focus[es] on" since the subject is "The most interesting study"

Sincerely,

Reviewer 1

Reviewer #2: In general, for the dynamical systems part I am satisfied. As for the interpretation, it is at least acceptable from my side. I must note however that the historical interpretations are not something I can really judge.

I suggest the peer reviews should be published such that it is clear that this was not checked by a historian.

I still think intrinsic and extrinsic Lyapunov Exponents is better terminology. Referring to a different paper that something similar was used is not a good argument. Again, I leave this to the editor.

I went through the text and especially the changes. I found one minor issue:

Line 235; looking at Figure 3 panel 2 I observe two saddles, one on the vertical axis, and a "positive" one within the first quadrant. So perhaps be even more careful indicating the "positive" one? Also, the trajectories forming the stable manifold will approach the saddle but never reach it. So I suggest to write "that approach the saddle".

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Reviewer #1: No

Reviewer #2: No

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A THEORETICAL ANALYSIS OF COMPLEX ARMED CONFLICTS

PONE-D-20-37260R3

Dear Dr. Della Rossa,

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PLOS ONE

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