Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent

Round 1

Reviewer 1 Report

Dear authors, could you change :

- magnify the picture Fig. 7 b.

- page 10: change description: Figure8. Xxxx to Figure 8. Xxxxx  (with space between Figure and number of figure).

- page 11: change Figure9. Yyyy to Figure 8. Yyyy  (with space).

- references include many old publications - 2, 4 ,6, 7 (from 1976 !!!), 8, 9, 10, 17, 18, 20, 21 = publications older than 20 years should not be in the reference list.

Comments for author File: Comments.pdf

Author Response

Reviewer #1

Thank you for your review. 

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear authors!

Thank you for the brilliant paper. It is very interesting to read your study on applying an AI approach to the analysis of chaotic behavior. The achieved accuracy of chaotic regime distinguishing is good, and the research is presented rather clearly.

Nevertheless, some remarks can be made.

1. It is quite necessary to compare the proposed approach with any existing ones. For example, the paper "Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods", 2010, shows that simple recurrence-based measures like determinism can provide information on whether the behavior is chaotic without estimates of Lyapunov
exponents. An approach based on clustering is proposed in "Bifurcation and recurrent analysis of memristive circuits", 2018. The paper "Transformation-cost time-series method for analyzing irregularly sampled data", 2015, proposes TACTS method.

What is the advantage of using complicated CNN comparing to determinism, cluster number, or any other much simpler measure?

2. Please, replace the linear scale in Y-axis with the logarithmic scale in Fig. 6 and Fig. 11. Otherwise, they look not informative.

The main drawback of the paper is considering the AI-based approach as an extension of RQA, which is designed so as it is not necessary to use anything in addition to it. Moreover, CNN is much more computationally elaborate than RQA measures.
But, if your RQA + CNN approach would appear more efficient, it would mean a new era of RQA, nevertheless, this needs proper investigation.

So, I am looking forward to new version of your manuscript. I Hope, it will find its reader after the revision.

Author Response

Reviewer #2

Thank you for your review. 

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear authors!

 

Thank you for improving the paper. While the paper text was not corrected extensively, the reply is rather convincing.

I think the paper may be accepted in the present form.