Global Attractivity of Symbiotic Model of Commensalism in Four Populations with Michaelis–Menten Type Harvesting in the First Commensal Populations
Round 1
Reviewer 1 Report
1. You should describe clearly the main question addressed by the research. Please improve the abstract specifying the main objectives of the work.
2. Please include the definition of the main notion of global stability used in the work. Apply it to the system (1).
3. It is not clear why you use the notion of "global attractivity" for the continuous-time system. In this case, they use the notion of "global stability". "Attractivity" is related to the system with discrete time.
4. What specific gap in the field is addressed by your work? As far as I see, you use the comparison principle combined with Lyapunov functions in order to get the stability results. Why not use Lyapunov functions directly? What is the advantage of your method?
5. What does the work add to the subject area of population dynamics compared with other published material?
6. When analyzing the related works from the field of population dynamics, you should describe the role of using time delays for modeling populations, e.g. 10.1016/j.ijnonlinmec.2020.103630 , 10.3389/fevo.2021.531833
7. The conclusions should be extended by added comparison of your results with some related works.
8. The quality of the Fig.1-7 should be improved (font size greater). Please extend the captions to the figures by adding the description of the quality behavior observed.
9. You present only the stable behavior with the help of numerical experiments. Please add examples of unstable behavior, when your stability conditions are violated.
Author Response
Dear Sir,
Thank you for your carefully reading of our paper, we had carefully revised the paper according to your comments.
- Comment: You should describe clearly the main question addressed by the research. Please improve the abstract specifying the main objectives of the work.
Reply: We had revised the Abstract part and almost all of the introduction section.
- Comment: Please include the definition of the main notion of global stabilityused in the work. Apply it to the system (1).
Reply: Thank you for point out this, indeed, we had carefully read the book and some of the paper again, and try to discuss this matter with Prof. Fengde Chen in Fuzhou University. Now, we add the definition of globally attractive on the Section 2.
- Comment: It is not clear why you use the notion of "global attractivity" for the continuous-time system. In this case, they use the notion of "global stability". "Attractivity" is related to the system with discrete time.
Reply. It is our opinion that by using the Lyapunov function, we could draw the conclusion of globally stable, however, by using the comparison theorem, it is more suitable say it “globally attractive”;
- Comment: What specific gap in the field is addressed by your work? As far as I see, you use the comparison principle combined with Lyapunov functions in order to get the stability results. Why not use Lyapunov functions directly? What is the advantage of your method?
Reply: Thank you for point out this, we carefully revise the introduction section, and pointed out that our system could not apply Lyapunov function directly, otherwise, the results needs some extra assumption, which is not the essential one.
- Comment: What does the work add to the subject area of population dynamics compared with other published material?
Reply: Thank you for propose this question, I think there are seldom scholars investigated the multi species commensalism model, and we put forward some work on this direction, maybe our work will bring more scholars done works on this direction.
- Comment: When analyzing the related works from the field of population dynamics, you should describe the role of using time delays for modeling populations, e.g. 10.1016/j.ijnonlinmec.2020.103630 , 10.3389/fevo.2021.531833
Reply: We had added these two paper in our new references. See [42,43].
- Comment:The conclusions should be extended by added comparison of your results with some related works.
Reply: We revised the conclusion part. Thank you for this question, such that we have to consider the contribution of other studies.
- Comment: The quality of the Fig.1-7 should be improved (font size greater). Please extend the captions to the figures by adding the description of the quality behavior observed.
Reply: Thank you for your question, we had rearrange the pictures, hope this time everything are O.K.
- Comment: You present only the stable behavior with the help of numerical experiments. Please add examples of unstable behavior, when your stability conditions are violated.
Reply: This is really an interesting question, to answer this question, we delete the Example 5.2 on the original paper, and then take r1 as the parameter to be considered, by choosing different type of parameter, we really observe some new findings.
To sum up, I think your comments are valuable, and it make our paper improved essentially. Now, is it possible of invite you as one of the authors of our paper? I really think your comments deserved you as one of the author of the paper.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
See the attached report.
Comments for author File: Comments.pdf
Author Response
Dear Sir,
We had carefully revise the paper according to your guidance.
We revise the tile, abstract, introduction and conclusion part. We add references [40-45] to cite the paper you mentioned.
Hope this time everything are O. K.
Round 2
Reviewer 1 Report
All my comments have been addressed in the revised version of the paper
Author Response
Dear Sir,
We had revised the paper according to your comments. We had highlight the corresponding part as red color.
Yours sincerely
Lili Xu
Author Response File: Author Response.pdf
