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Mathematics
Volume 9
Issue 24
10.3390/math9243287
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Article
Peer-Review Record

Analytic Matrix Method for Frequency Response Techniques Applied to Nonlinear Dynamical Systems I: Small and Medium Amplitude Oscillations

Mathematics 2021, 9(24), 3287; https://doi.org/10.3390/math9243287
by Elena Hernandez 1, Octavio Manero 2, Fernando Bautista 3 and Juan Paulo Garcia-Sandoval 1,*
Reviewer 1: Anonymous
Reviewer 2: Anonymous
Reviewer 3: Anonymous
Mathematics 2021, 9(24), 3287; https://doi.org/10.3390/math9243287
Submission received: 14 November 2021 / Revised: 13 December 2021 / Accepted: 15 December 2021 / Published: 17 December 2021
(This article belongs to the Section Dynamical Systems)

Round 1

Reviewer 1 Report

The method presentyed by the auyhors may be of interest in the field of large amplitudes. As for areas with small and medium amplitudes the available proven methods work quite well here. The solutions obtained  for large amplitudes are of interest, but  these solutions should be supplemented with stability analysis at small perturbations.

The paper presentation is filled with abbreviations such as: SAO, MAO, LAO and so on whch makes it very difficult to read.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The topic of research considered in the paper is interesting. However, I do have several comments:
1. Why did the authors choose the title to be "Analytic Matrix Method for Frequency Response Techniques Applied to Nonlinear Dynamical Systems I: Small and Medium Amplitude Oscillations"? To be precise, what does "I" mean? Will there be a second, i.e. "II" version? What differentiates between "I" and "II"?
2. I wonder how the proposed method can be extended to discrete-time nonlinear systems.
3. Can the authors provide examples of more realistic and practical systems? For instance, in the study of synchronization of thermostatically controlled loads as well as battery electric vehicles charging systems? Please discuss.
4. Again, using a second-order system is not enough. The authors should have considered examples with higher-order systems.
5. Please have a conclusion section and clearly state the limitations of the proposed method (if any).
 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper needs improvement, the following corrections are necessary:

  1. The abstract should briefly add relevant information about the results and conclusions. Se debe mejorar el abstract.
  2. Paragraph 3 of the introduction has no bibliographic citations.
  3. It is necessary to improve the state of the art with papers related to the research topic.
  4. The problem statement needs to be improved.
  5. The introduction should be greatly improved since the objectives of the research are not clear and the contributions of the research are not seen either.
  6. Equation 56b has the points overlapping.
  7. If possible take show more results using more initial conditions.
  8. If it is possible to add results by varying any parameter of the system.
  9. Conclusions are needed.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Thanks for the corrections

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