Dynamic Analysis and Audio Encryption Application in IoT of a Multi-Scroll Fractional-Order Memristive Hopfield Neural Network

Round 1

Reviewer 1 Report

Please see the attached file.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript fails by considering numerical integration of piece-wise continuous functions

Thus, while the system (8) is indeed continuous (functions atan are continuous), the considered system in this manuscript (a modification of (8)) is not continuous, due to the function

h(w)=w- ∑sgn(w + (2i - 1)) + sgn(w-(2i - 1))

Or, as known, all numerical methods, for both IO and FO differential equations, require continuity

By using any implemented routine for such discontinuous systems (e.g. in matlab, and in many other software) one obtains a result, but this is a "sewing"-like of the correct solutions before and after the discontinuity manifold. Therefore, in these cases, due to the discontinuity, the solution is not correct. 

A possible way to avoid this problem which, indeed, appears in several publications, is to modify the function  h

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors propose an audio encryption application based on a non-ideal flux-controlled memristive Hopfield neural network model (FMHNN) via Caputo derivative. They show different multi-scroll attractors by changing the parameters of the FMHNN.

Based on my observation, the work proposal is attractive, and the results can be of great importance if the authors follow the following modifications or corrections:

1. The authors must list the main contributions of their work and establish a context for future results and possible applications.
2. If the system (11) is fractional, why does the Jacobian matrix (14) not? Does the non-integer order has no influence?
3. In line 119, the authors say the system is chaotic if it has a real root and two complex conjugate roots. How do the authors support this?
4. There are typo errors in line 156, "attrctors", line 164, "attracotrs".
5. For Fig. 7 (c), how do the authors conclude that the depicted dynamics are chaotic? Please apply the 0-1 test to support this.

I could recommend this paper for publication after the above revisions.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

In this paper, the fractional-order definition of Caputo is introduced based on a nonideal 1 flux-controlled memristive Hopfield neural network model, when changing the parameters of the 2 fractional-order memristive Hopfield neural network (FMHNN) can generate a different amount 3 of multi-scroll attractors. Some dynamical behaviors are investigated by numerical simulation, 4 especially analyzed coexistence and bifurcation under different order and different coupling strength. 5 The results show that the chaotic system of FMHNN has abundant dynamic behaviors. In addition, a 6 chaotic audio encryption scheme under MQTT protocol is proposed and implemented by Raspberry 7 Pi, the audio encryption system based on FMHNN has a broad future in intelligent home and other 8 IoT application.

The reviewer has the following concerns that should be addressed in order to improve the quality of the paper:

1. The motivation on the study should be further emphasized, particularly; the main advantages of the results in the paper comparing with others should be clearly demonstrated.
2. English should be further improved, since the paper has some spelling and grammar errors. Also, the paper has some editing problems.
3. The example section needs to be further expanded and including some remarks to show the effectiveness and efficiency of the proposed method, compared with others.
4. Some remarks on Theorem 1 would be necessary and helpful.
5. It seems that the technique of this paper is well-known. The authors must clearly show the difference and improvements in comparison with the existing results in the view of technique analysis.
6. Explain the feasibility of the results from the implementation and computational point of view. Some remark words on computation complexity of the results should be given.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

This paper can be accepted. 

Author Response

Dear reviewer,

Thank you very much for your recognition of our paper. Thank you again for your hard work!

Sincerely,

Fei 

Reviewer 2 Report

My main concern was solved

Author Response

Dear reviewer,

Thank you very much for your recognition of our paper. Thank you again for your hard work!

Sincerely,

Fei Yu 

Reviewer 4 Report

All my concerns have been satisfactorily addressed in the revised version. So I suggest that this paper can be accepted in the journal in its present form.

Author Response

Dear reviewer,

Thank you very much for your recognition of our paper. Thank you again for your hard work!

Sincerely,

Fei Yu