Synchronization of Fractional-Order Uncertain Delayed Neural Networks with an Event-Triggered Communication Scheme

Round 1

Reviewer 1 Report

The paper investigates a methodology for designing event triggered synchonization of fractional order uncertain delayed RNNs,  and presents four numerical examples to confirm the effectiveness of the theoretical results. However, in the section 4, only the values of parameters are given,  it is suggested to add the graphics and figures to visually represent the synchonization results. In addion, the English writting, formulas and other details should be corrected and polished. 

For examples, 

In Abstract, 'two numerical examples has been...' should be 'four numerical examples have been...'.

In Theorem 1, R6 > 0 repeats three times.

In (10) and (11) ...

Author Response

Response to Reviewer 1 Comments

 

Point 1: I found that sections 2 & 3 should be re‐organized and be shortened. It may be easier for the readers if the authors define properly the mixture of regression model and the class‐ membership equation first before moving to the computation of the GINI and of the Polarization of subgroups. Sections 2.1 and 2.2 are too long and can be significantly reduced. In section 2.1 the authors assume the condition u_k > u_j, but this does not appear anywhere else in the calculation of the mixture of regression model. After equation (10) all the other equations are not numbered.

 

Response 1: I have already made the corrections as suggested by the Reviewer in the attachment.

 

Point 2: The probability for a given country h to be in a class k should be the proportion of observations (households) in country h that belong to the income class k. On page 9, the first equation (it would be easier for the reader if the equation is numbered) is not exactly the proportion of people because the authors take the sum of the probability. The interpretation of the equation in not obvious. Normally, after estimating a mixture of regression model we have for each observation its estimated probabilities to be classified into the different classes identified. What is often done is to classify a given observation into the class where its estimated probability is higher. In many software this is also the method used that gives us the proportion of people in each of the classes. The authors should explain the equation on page 9 and how to interpret it. Alternatively, they may use the proportion approach which will make the interpretation easier.

 

Response 2: I have already made the corrections as suggested by the Reviewer in the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper, event-triggered synchronization of fractional order uncertain recurrent neural networks with delays is investigated. The topic of the paper is interesting but novelty is not clear and sufficient. However, to improve the quality of the manuscript the following comments should be considered into the account.

v In the introduction, the authors are suggested to describe the research gap more clearly.

v At the end of the Introduction, authors should supplement the organization of the paper and notation section.

v How does the LKF constructed in this paper affect the realization of the goal of this paper? That is, how the conservatism of the stability criterion derived in this paper affects the control objectives of this paper.

v Significance of constructing this LKF is not discussed anywhere. Provide some comparative analysis.

v A comparative simulation of relevant research results should be added to enhance the persuasion of this paper. Also, graphical representation of simulation results are strongly recommended.

v What are the difficulties in this study? The authors are encouraged to add how their work is not a collection of ideas from existing results.

Author Response

In this paper, event-triggered synchronization of fractional order uncertain recurrent neural networks with delays is investigated. The topic of the paper is interesting but novelty is not clear and sufficient. However, to improve the quality of the manuscript the following comments should be considered into the account.

 In the introduction, the authors are suggested to describe the research gap more clearly.

 At the end of the Introduction, authors should supplement the organization of the paper and notation section.

How does the LKF constructed in this paper affect the realization of the goal of this paper? That is, how the conservatism of the stability criterion derived in this paper affects the control objectives of this paper.

 Significance of constructing this LKF is not discussed anywhere. Provide some comparative analysis.

 A comparative simulation of relevant research results should be added to enhance the persuasion of this paper. Also, graphical representation of simulation results are strongly recommended.

 What are the difficulties in this study? The authors are encouraged to add how their work is not a collection of ideas from existing results.

Response I have already made the corrections as suggested by the Reviewer in the attachment.

 

Author Response File: Author Response.docx

Reviewer 3 Report

This paper considers event-triggered synchronization of fractional order uncertain recurrent neural networks with delays by using linear matrix inequalities. The author mention “ensure the stochastic stability” in Abstract, but what I don't see in the text is stochastic stability. Mathematical notation is too messy for readability. The references are all pre-2019 and don't reflect the latest research. So my opinion is negative.

Author Response

This paper considers event-triggered synchronization of fractional order uncertain recurrent neural networks with delays by using linear matrix inequalities. The author mention “ensure the stochastic stability” in Abstract, but what I don't see in the text is stochastic stability. Mathematical notation is too messy for readability. The references are all pre-2019 and don't reflect the latest research. So my opinion is negative.

Response : I have already made the corrections as suggested by the Reviewer in the attachment.

 

Author Response File: Author Response.pdf

Reviewer 4 Report

The authors studied Synchronization of fractional order uncertain delayed neural networks with a event-triggered communication scheme. I have the following comments. 

1. In introduction, the object of this paper is very ambiguous. Authors should revise or add to represent the object of this paper in introduction.

2. Many parameters are not introduced before, therefore not to understand.

3. What is differentiation compare to other paper, please add it.

4. How to define Lyapunov Krasovskii functional? Also, I would expect that the authors can provide some simulation results.

5. The paper needs a careful proofreading to correct typos and improve the text, as in the following examples: “3mainresults” “two numerical examples has been presented to confirm the effectiveness of the main results.”……..

6. The authors could improve Abstract and Conclusion. Also, poor English language makes the paper very hard to follow.

Comments for author File: Comments.pdf

Author Response

The authors studied Synchronization of fractional order uncertain delayed neural networks with a event-triggered communication scheme. I have the following comments. 

1. In introduction, the object of this paper is very ambiguous. Authors should revise or add to represent the object of this paper in introduction.
2. Many parametersare not introduced before, therefore not to understand.
3. What is differentiation compare to other paper, please add it.
4. How to define Lyapunov Krasovskii functional? Also, I would expect that the authors can provide some simulation results.
5. The paper needs a careful proofreading to correct typos and improve the text, as in the following examples:“3mainresults”“two numerical examples has been presented to confirm the effectiveness of the main results.”……..
6. The authors could improve Abstract and Conclusion. Also, poor English language makes the paper very hard to follow.

Response : I have already made the corrections as suggested by the Reviewer in the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors did not add visual simulation results as suggested.

Author Response

Paper ID:fractalfract-1887968 Title: Synchronization of fractional order uncertain delayed neural networks with a event-triggered communication scheme
Comments from the editors and reviewers: Reviewer #1:
Comment: 1. The authors did not add visual simulation results as suggested. Response: As per reviewer suggestion we tried the simulation work but cannot able to get the good results. We will try in future.

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper has been well revised. I would like to recommend this paper to be published.

Author Response

Paper ID:fractalfract-1887968 Title: Synchronization of fractional order uncertain delayed neural networks with a event-triggered communication scheme Comments from the editors and reviewers: Reviewer # 3
Comment: 1. This paper has been well revised. I would like to recommend this paper to be published.
Response: We thank the reviewer for his constructive comments and efforts.

Author Response File: Author Response.pdf