Chaos Controllability in Fractional-Order Systems via Active Dual Combination–Combination Hybrid Synchronization Strategy
Round 1
Reviewer 1 Report
In the current work, the authors investigated a dual combination-combination hybrid synchronization in eight non-identical fractional-order chaotic systems with distinct dimensions using active control methodology.
Using the scaling matrix, the considered synchronization technique is attained between fractional complex chaotic systems and fractional hyperchaotic systems.
The results are new, novel and very interesting especially the numerical simulation which was presented to confirm the sufficiency and effectiveness of proposed DCCHS scheme.
I recommend the acceptance of the paper for publication in Fractal Fract.
Author Response
Thank you very much for providing acceptance recommendation for publication in Fractal Fract.
Reviewer 2 Report
see attachment
Comments for author File: 
Comments.pdf
Author Response
First of all we express our cordial gratitude for the valuable and constructive review of our paper. The reviewer’s comments are indeed quite helpful to further strengthen the overall quality of the paper. With utmost care, we have incorporated all suggestions/corrections as proposed by the reviewers. The specific responses to the comments of the reviewers are listed below.
Comment 1: Some grammatical and spelling mistakes in the manuscript should be carefully checked.
Answer: As suggested, we have checked throughout the paper very carefully and made corrections.
Comment 2: In the Abstract, the author mentioned that DCCHS scheme can provide higher protection for secure communication. Are there any practical examples to illustrate?
Answer: We have described some applications of "synchronization" in engineering as well as in secure communication with proper citations in the introduction in revised manuscript. (Page no. 1, second paragraph in introduction).
Comment 3: The article needs to provide enough Remarks to highlight the advantages of your manuscript in contrast to the existing papers.
Answer: We have agreed with the comments. As suggested, we have added enough Remarks to highlight the advantages of our manuscript in contrast to the existing papers. We have also updated the motivation part in the introduction in revised manuscript. (Page no. 2, Fourth and Sixth paragraphs in introduction).
Comment 4: In Figure 3, the author describes ’The error dynamics Eij (t), i = 1, 2, j = 1, 2, 3, 4 of master and slave systems with controllers’, but no E21, E22, E23, E24 are found in the figure.
Answer: We have made the changes in Figure 3 as per the suggestion given. (Page no. 12 in Numerical Simulation).
Comment 5: Please unify the format of references according to the requirements of journal.
Answer: As pointed out by the reviewer, we have unified the format of references according to the requirements of journal.
Again we are grateful to all the reviewers for their comments and suggestions provided.
Reviewer 3 Report
Fractalfract- 2018005
Title: Chaos Controllability in Fractional-Order Systems via Active Dual Combination-Combination Hybrid Synchronization Strategy
In this paper, the dual combination-combination hybrid synchronization (DCCHS) scheme is investigated in fractional-order chaotic systems with a distinct dimension applying a scaling matrix. The formulations for the active control is analyzed numerically using Lyapunov’s stability analysis in order to achieve the proposed DCCHS among the considered systems. Mathematical simulations are implemented using MATLAB and confirm that the proposed approach is superior and effective in comparison to existing chaos literature.
In the reviewer’s opinion the paper has several problems and needs to be rewritten. The most arguable choice you have made concerns Table 1 where you compare your paper with papers of several other authors with equivalent research using different methods. That is quite inappropriate. You can compare methods and numerical examples of their application, nothing further.
I recommend that you rewrite your paper taking good attention and providing a description of all the methods you intend to compare, enhancing the method you propose. Restrict yourself to highlight only scientific work. Take also some care in the English language writing.
Author Response
First of all we express our cordial gratitude for the valuable and constructive review of our paper. The reviewer’s comments are indeed quite helpful to further strengthen the overall quality of the paper. With utmost care, we have incorporated all suggestions/corrections as proposed by the reviewers. The specific responses to the comments of the reviewers are listed below.
Comment 1: In the reviewer’s opinion the paper has several problems and needs to be rewritten. The most arguable choice you have made concerns Table 1 where you compare your paper with papers of several other authors with equivalent research using different methods. That is quite inappropriate. You can compare methods and numerical examples of their application, nothing further.
Answer: The advantage of DCCHS scheme of coupled complex fractional chaotic systems takes minimum synchronization time in comparison to the previously existing synchronization schemes, which is shown in subsection 5.1 and too much time and energy would be saved for our future practical applications.
Comment 2: I recommend that you rewrite your paper taking good attention and providing a description of all the methods you intend to compare, enhancing the method you propose. Restrict yourself to highlight only scientific work. Take also some care in the English language writing.
Answer: We have agreed with the comments. As suggested, we have updated the motivation part in the introduction in revised manuscript. (Page no. 2, Fourth and Sixth paragraphs in introduction).
We have also made the necessary corrections in the paper as per the suggestion given.
Again we are grateful to all the reviewers for their comments and suggestions provided.
Round 2
Reviewer 2 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
Thank you very much for providing recommendation to publish in Fractal Fract.
Reviewer 3 Report
The paper is significantly improved, and the comparison of the authors was eliminated from table 1.
21% of the references correspond to one of the authors of this paper. I believe this is too much and should be corrected.
The paper has some typos or English incorrections that I am pointing:
- page 2, line 32 “have” instead of “has”,
- page 2, line 40, “two master” instead of “two or master”,
- page 2, line 50, “is basically s …” (you should rewrite this),
- page 2, line 67, “T-system, Lu system”,
- page 4, in the first line of the proof of theorem 1 I think you are referring equation (14) and not (15),
- page 7, equation 22, in the first equation you have an extra “)”, and in the text before equation (23) it is “described” instead of “prescribed”,
- page 9, line 148 “Phase” doesn’t need a capital letter,
-page 9, line 149, please correct the first expression,
- page 10, please rewrite (e) in the legend,
- page 12, line 154, please verify the formatting.
Author Response
Thank you very much for providing comments and suggestions to improve our manuscript. We have included all comments and suggestions accordingly.
Please see red color in updated manuscript.
Author Response File: Author Response.pdf
